A lot of it will depend on what type of lighting you want. Are you looking for ambient, mood lighting to guide someone to the sink or fridge at night, or are you looking for functional lighting that will help you see better to cook, etc?
If you are looking for ambient lighting, there are a variety of LED "puck" lights (small round lights) that ussually plug into an outlet. These will be the easiest to install and they are fantastic because you'll replace the fixture before you replace the bulb. They come in several colors, white and amber lights being the most common but you can get "colors" like red or blue as well. They can be used above or under your cabinets. They don't get warm, so you don't have to worry about leaving them on for long periods of time (or little fingers getting burned if you have kids) The hardest part is "hiding" the wires. One way to do this is to put an outlet inside a cabinet and drill a hole to put the wires into.
If you are looking for functional lighting, you can use puck lighting but use halogen instead. The bulbs don't last the way LED's do but the light is brighter, the down side is they get just as hot as a standard lightbulb. You can also use flourscent strip lighting, these also do not get as hot. These types of lights typically come in plug in but if you look around you can find hardwired ones.
I have puck lights under my cabinets near the sink and they work out great! And they aren't that difficult to install.
Managed an electrical department