Your question was. How does ILS (instrument Landing System) work.
Principle of Operation
An ILS consists of two independent sub-systems, one providing lateral guidance (Localizer), the other vertical guidance (Glideslope or GlidePath) to aircraft approaching a runway.
The emission patterns of the localizer and glideslope signals. Note that the glideslope beams are partly formed by the reflection of the glideslope aerial in the ground plane.A localizer (LOC, or LLZ in Europe) antenna array is normally located beyond the departure end of the runway and generally consists of several pairs of directional antennas. Two signals are transmitted on a carrier frequency between 108 MHz and 111.975 MHz. One is modulated at 90 Hz, the other at 150 Hz and these are transmitted from separate but co-located antennas. Each antenna transmits a fairly narrow beam, one slightly to the left of the runway centreline, the other to the right.
The localizer receiver on the aircraft measures the Difference in the Depth of Modulation (DDM) of the 90 Hz and 150 Hz signals. For the localizer, the depth of modulation for each of the modulating frequencies is 20 percent. The difference between the two signals varies depending on the position of the approaching aircraft from the centreline.
If there is a predominance of either 90Hz or 150Hz modulation, the aircraft is off the centreline. In the cockpit, the needle on the Horizontal Situation Indicator, or HSI (The Instrument part of the ILS), will show that the aircraft needs to fly left or right to correct the positional error to fly down the centre of the runway. If the DDM is zero the receiver aerial and therefore, the aircraft, is on the centreline of the localizer coinciding with the physical runway centreline.
A glideslope or Glidepath (GP) antenna array is sited to one side of the runway touchdown zone. The GP signal is transmitted on a carrier frequency between 328.6 MHz and 335.4 MHz using a technique similar to that of the localizer, the centreline of the glideslope signal being arranged to define a glideslope at approximately 3° above the horizontal.
Localizer and glideslope carrier frequencies are paired so that only one selection is required to tune both receivers.
These signals are displayed on an instrument in the cockpit. The pilot controls the aircraft so that the indications on the instrument remain centered on the display. This ensures the aircraft is following the ILS centreline. Some aircraft possess the ability to route signals into the autopilot, which allows the approach to be flown automatically by the autopilot.
Localizer array and approach lighting at Whiteman Air Force Base, Johnson County, Missouri.In addition to the previously mentioned navigational signals, the localizer provides for ILS facility identification by periodically transmitting a 1020 Hz morse code identification signal. For example, the ILS for runway 04R at John F. Kennedy International Airport transmits IJFK to identify itself to users whereas runway 04L is known as IHIQ. This lets users know the facility is operating normally and that they are tuned to the correct ILS. The glideslope transmits no identification signal and relies on the localizer for identification.
Modern localizer antennas are highly directional. However, usage of older, less directional antennas allows a runway to have a non-precision approach called a localizer back course. This lets aircraft land using the signal transmitted from the back of the localizer array. This signal is reverse sensing so a pilot may have to fly opposite the needle indication (depending on the equipment installed in the aircraft). Highly directional antennas do not provide a sufficient signal to support a backcourse. In the United States, backcourse approaches are commonly associated with Category I systems at smaller airports that do not have an ILS on both ends of the primary runway.
 Marker Beacons
The NDB station co-located with Middle Marker of Beijing Capital International Airport ILS RWY36LMain article: Marker beacon
On most installations marker beacons operating at a carrier frequency of 75 MHz are provided. When the transmission from a marker beacon is received it activates an indicator on the pilot's instrument panel and the modulating tone of the beacon is audible to the pilot. The correct height the aircraft should be at when the signal is received in an aircraft is promulgated.
 Outer Marker
The outer marker should be located 7.2 km (3.9 NM) from the threshold except that, where this distance is not practicable, the outer marker may be located between 6.5 and 11.1 km (3.5 and 6 NM) from the threshold. The modulation is repeated Morse-style dashes of a 400 Hz tone. The cockpit indicator is a blue lamp that flashes in unison with the received audio code. The purpose of this beacon is to provide height, distance and equipment functioning checks to aircraft on intermediate and final approach. In the United States, an NDB is often combined with the outer marker beacon in the ILS approach (called a Locator Outer Marker, or LOM); in Canada, low-powered NDBs have replaced marker beacons entirely.
 Middle Marker
The middle marker should be located so as to indicate, in low visibility conditions, the missed approach point, and the point that visual contact with the runway is imminent, Ideally at a distance of 1050m from the threshold. It is modulated with a 1300 Hz tone as alternating dots and dashes. The cockpit indicator is an amber lamp that flashes in unison with the received audio code.
 Inner Marker
The inner marker, when installed, shall be located so as to indicate in low visibility conditions the imminence of arrival at the runway threshold. This is typically the position of an aircraft on the ILS as it reaches Category II minima. The modulation is Morse-style dots at 3000Hz. The cockpit indicator is a white lamp that flashes in unison with the received audio code. The audio code gets faster and higher in frequency, the closer the aircraft gets to the airport.
Distance Measuring Equipment (DME) is replacing markers in many installations. This provides more accurate and continuous monitoring of correct progress on the ILS to the pilot, and does not require an installation outside the airport boundary. The DME is frequency paired with the ILS so that it is automatically selected when the ILS is tuned. It gives pilots a slant range measurement of distance to the runway in nautical miles.
It is essential that any failure of the ILS to provide safe guidance is detected immediately by the pilot. To achieve this, monitors continually assess the vital characteristics of the transmissions. If any significant deviation beyond strict limits is detected, either the ILS is automatically switched off or the navigation and identification components are removed from the carrier.  Either of these actions will activate an indication ('failure flag') on the instruments of an aircraft using the ILS.
 Approach Lighting
Some installations include medium or high intensity approach light systems. Most often, these are at larger airports. The Approach Lighting System (abbreviated ALS) assists the pilot in transitioning from instrument to visual flight, and to align the aircraft visually with the runway centreline. At many non-towered airports, the intensity of the lighting system can be adjusted by the pilot.
 Use of the Instrument Landing System
At large airports, Air Traffic Control will direct aircraft to the localizer via assigned headings, making sure aircraft do not get too close to each other (maintain separation), but also avoiding delay as much as possible. Several aircraft can be on the ILS at the same time, several miles apart. An aircraft that has intercepted both the localizer and the glideslope signal is said to be established on the approach. Typically, an aircraft will be established by 6 nautical miles from the runway.
 Decision Altitude/Height
Once established on an approach, the (auto)pilot will follow the ILS and descend along the glideslope, until the Decision Altitude is reached (for a typical Category I ILS, this altitude is 200 feet above the runway). At this point, the pilot must have the runway or its approach lights in sight to continue the approach. If neither can be seen, the approach must be aborted and a Missed Approach procedure will be initiated, where the aircraft will climb back to a predetermined altitude. From there the pilot will either try the same approach again or divert to another airport.
 ILS categories
There are three categories of ILS which support similarly named categories of operation.
Category I - A precision instrument approach and landing with a decision height not lower than 60 m (200 ft) above touchdown zone elevation and with either a visibility not less than 800 m or a runway visual range not less than 550 m. An aircraft equipped with an Enhanced Flight Vision System may, under certain circumstances, continue an approach to CAT II minimums. [14 CFR Part 91.175 amendment 281]
Category II - Category II operation: A precision instrument approach and landing with a decision height lower than 60 m (200 ft) above touchdown zone elevation but not lower than 30 m (100 ft), and a runway visual range not less than 350 m.
Category III is further subdivided
Category III A - A precision instrument approach and landing with: a) a decision height lower than 30 m (100 ft) above touchdown zone elevation, or no decision height; and b) a runway visual range not less than 200 m.
Category III B - A precision instrument approach and landing with: a) a decision height lower than 15 m (50 ft) above touchdown zone elevation, or no decision height; and b) a runway visual range less than 200 m but not less than 50 m.
Category III C - A precision instrument approach and landing with no decision height and no runway visual range limitations. A Category III C system is capable of using an aircraft's autopilot to land the aircraft.
In each case a suitably equipped aircraft and appropriately qualified crew are required. For example, Cat IIIc a fail operational system is required, Cat I does not. A Head-Up Display which allows the pilot to perform aircraft maneuvers rather than an automatic system is considered as fail operational. Cat I only goes off of altimeter indications for decision height, the Cat II and Cat III approaches go off the radar altimeter for a decision height
(Reference ICAO Annex 10 AERONAUTICAL TELECOMMUNICATIONS Volume 1 RADIO NAVIGATION AIDS 2.1.1)
An ILS is required to shut down upon internal detection of a fault condition as mentioned in the monitoring section. With the increasing categories, ILS equipment is required to shutdown faster since higher categories require shorter response times. For example, a Cat I localizer must shutdown within 10 seconds of detecting a fault, but a Cat III localizer must shutdown in less than 2 seconds. 
 Limitations and alternatives
The Glideslope station at Hanover/Langenhagen International Airport in Hanover, Germany.Due to the complexity of ILS localizer and glideslope systems, there are some limitations. Localizer systems are sensitive to obstructions in the signal broadcast area like large buildings or hangars. Glideslope systems are also limited by the terrain in front of the glideslope antennas. If terrain is sloping or uneven, reflections can create an uneven glidepath causing unwanted needle deflections. Additionally, since the ILS signals are pointed in one direction by the positioning of the arrays, ILS only supports straight in approaches. Installation of ILS can also be costly due to the complexity of the antenna system and siting criteria.
In the 1970s there was a major US & European effort to establish the Microwave Landing System, which are not similarly limited and which allow curved approaches. However, a combination of slow development, airline reluctance to invest in MLS, and the rise of GPS has resulted in its failure to be widely adopted. The Transponder Landing System (TLS) is another alternative to an ILS that can be used where a conventional ILS will not work or is not cost-effective.
Tests of the ILS system began in 1929, and the Civil Aeronautics Administration (CAA) authorized installation of the system in 1941 at six locations. The first landing of a scheduled U.S. passenger airliner using ILS was on January 26, 1938, as a Pennsylvania-Central Airlines Boeing 247-D flew from Washington, D.C., to Pittsburgh and landed in a snowstorm using only the Instrument Landing System.
The advent of the Global Positioning System (GPS) provides an alternative source of guidance for aircraft. The Wide Area Augmentation System (WAAS) will provide guidance to Category I standards beginning 2007. Other methods of augmentation are in development to provide for Category III minimums or better, such as the Local Area Augmentation System (LAAS).