There are several methods used for measurement of algae in water. These fall into three categories 1) numerical, that is, the number of cells present; 2) gravimetric, the wet or dry weight of cells present and 3) proximate, the amount of some cellular constituent such as chlorophyll, or protein. Most methods are simple but few are easy because they require some laboratory equipment. They also depend on what kind of 'concentration' you need. The method will depend on whether you want to know what kind of algae is present, how much is present, or how much of each kind.
NUMERICAL: cell counting:
Probably the oldest method is cell counting and it requires the most common of lab equipment--a microscope. This method has been used since the invention of the microscope and discovery of the microscopic world by Antony van Leeuwenhoek in the late 1600s. (Leeuwenhoek wasn't even trained as a scientist, but was instead a businessman and inventor.)
Counting is usually used when scientists want to know WHICH algae are present as well as how many. It is done using counting chambers that hold a known amount of water and counting and identifying each cell. It requires a microscope and some knowledge of the taxonomy of algae. It is simple because all you have to do is count. It gets more complicated without any knowledge of algae identification.
The most common modern method of measuring the amount of algae (biomass) in water is the measurement of chlorophyll-a. Only photosynthetic organisms contain chlorophyll-a, so this removes any confusion over same-sized organisms that are not photosynthetic. This measurement requires either a fluorometer or a spectrophotometer. It is VERY simple if one of those pieces of equipment is available. Details of how to do this analysis are available in any standard method of water analysis.
GRAVIMETRIC: an almost no-equipment method:
Gravimetric methods are rarely used nowadays by scientists studying algae or aquatic systems since chlorophyll-a measurement has become the standard method, but it may be just what you need.
Take your sample and try to screen out any large organisms, like zooplankton, insect larvae etc.. Zooplankton are the tiny animals in the water that eat algae. Most (but not all) can be removed by screening with a mesh of approximately 150 micrometers. This size may remove some large algae, too. A very simple method is to allow the sample to settle in a graduated cylinder and measure the volume. This is faster if the cells are killed with alcohol, formalin or an iodine solution called Lugol's iodine — all are toxic to humans. Samples can be concentrated using a centrifuge, if that is available. The most efficient method is to filter the sample onto a pre-weighed filter then reweigh--the difference is the wet weight. To measure dry weight, filter onto a pre-weighed filter and dry the sample overnight in a low temperature oven (about 60 degrees C) then reweigh to get dry weight by difference.