Defining Extraterrestial Life
Scientists don't agree on a definition for life. There's even some dispute over what constitutes 'extraterrestrial'. After all, if life is found on Mars, for example, how will we know whether it developed on Mars or whether it originated from Earth? Let's assume that if something is extraterrestrial that it didn't come from Earth. How, then, do we define life? Most of the definitions found in biology texts are too broad to be used as a basis for a search. At present, the search involves looking for carbon-based (organic) molecules, water (preferably liquid), the presence of elements required for life on Earth, and structures that are formed from life processes (like cells). Not all organic molecules are associated with life: DNA, RNA, or proteins carry much more weight than benzene or methane. Limiting the list of chemicals related to life limits the places to look for such life. Heavy elements aren't found in very old star systems. Water isn't found on all planets and certainly not in all regions of planets that have it.
Developing a Strategy
A large part of the search is selecting the best tools for the job. Will samples be examined at the site (in situ) or brought back to Earth for analysis? Many of the most sensitive pieces of equipment that would be used on Earth aren't available in a form suitable for space missions. Factors such as size, cost, sensitivity, reliability, and power consumption all come into play. At this time, there isn't a recommended set of tests to be performed. The best bet seems to lie in using multiple techniques which offer a range of sensitivities and resolutions.
Looking in the Right Places
You can't find something if you aren't looking in the right place! However, most of the potential 'sweet spots' for life (under rocks, deep underwater, buried under ice, within canyons) aren't hospitable to space vehicles. When mission locations are selected, they represent a compromise between practicality and their ability to support potential life.
Avoiding Contamination
Spacecraft are generally sterilized so that they do not contaminate extraterrestrial locales with Earth organisms. However, the degree of the sterilization process varies. For example, The European Space Agency's Cassini probe was not sterilized to the same specifications as NASA's Mars Rovers because it was felt that the extreme cold to be experienced by Cassini would preclude contamination. Sterilization methods are mission-specific. Dry heating in an oven may work for some spacecraft, yet would destroy delicate equipment necessary for another.
The Process
A search for life on other planets tends to be a multi-phase endeavor, requiring reconnaissance from Earth or fly-by missions. Remote sensing is used to help identify the best places to look for life. Robotic sampling missions may then be attempted. Once a landing zone is selected, which can cover an enormous area, rovers can be used to deliver samplers closer to the best locations.

