|MadSci Network: Astronomy|
Sorry it took so long to answer your question, but I hope I can now provide you with some insight onto an interesting topic. First of all, there are two basic strategies for searching for extraterrestial life, and I will talk a little about both of them.
The first, and furthest (in distance), is a SETI program, in which astronomers comb radio telescope data for signs of signals from other worlds. In this case, the signal would more than likely have to come from an intelligent species, but as long as they are generating radio signals that we can detect, this type of hunt certainly isn't limited to conditions that we can imagine, since we do not know what environment the signals would originate from. You can actually use your computer at home to help analyze the mounds of data that one SETI program generates. There is a screen saver that will download packets of SETI data and process it on your computer when your screen-saver pops up. You can get information on the program, and how much data has been analyzed by visiting the SETI@home site.
As for how we examine life in the solar system, well, there are two parts to this. Number one, is that we look for life having conditions similar to Earth since we know for one, conditions like this obviously support life. We can certainly imagine alternative conditions, but there are infinitely more of those to examine than directing our limited resources to something we know works, namely Earth-like conditions. Secondly, it is only recently, that we have even begun to accept the idea that life could exist on places such as Mars and Europa, as we have discovered on Earth, bacteria that live deep underground, living off the heat of the Earth and chemicals in the lower crust, and bacteria that thrive in 200F degree water in hot springs. So, it is now clear, that life can survive in very harsh, but still Earth-like conditions.
Also, it is impossible for us to imagine something we cannot imagine. If there were a formula for a different type of life, we certainly don't know what it is, and therefore, couldn't create or identify what those conditions would be. If you want more information on these things, please check out some other answers I have given, and things other Mad Scientists have contributed. Thank you.
This post is about interstellar travel.
This post is about the long-term outlook for life in the Solar System.
This post is about the Martian meteorite that may contain signs of ancient life.
This post is about the prospect of life on Io and Europa, two Jovian moons.
You might also want to visit NASA and the SETI Institute.
A search for SETI on the MadSci search page will reveal about 100 documents and descriptions that may be of some use to you as well. Thanks for the question.
Try the links in the MadSci Library for more information on Astronomy.