Life as we know it is entirely carbon-based (made of molecules mostly composed of carbon atoms). Though we cannot presently imagine life forms that are not carbon-based, when searching for alien life it is good to keep our eyes open, in case our imagination has failed us!

By definition, life must engage in some form of metabolism - that is, it must engage in chemical reactions that run counter to equilibrium, or the balance, of what would happen if the lifeform was not there. This means we can search for life by looking for chemistry that is out of equilibrium or out of balance. For example, if aliens looked at Earth, they might notice that our atmosphere contains oxygen, as well as methane. These are two gases that normally would react with each other very quickly, leaving none in our atmosphere. In fact, oxygen and methane do react in our atmosphere all the time. The only reason that there is any of these two gases left on Earth is because something is constantly adding more oxygen and more methane back into our atmosphere. That something is life (specifically plants and other photosynthesizing organisms - oxygen - and bacteria and other methanogenic organisms - methane)!

This is not to limit ourselves to just looking for oxygen and methane, either. If we found a planet with substantial amounts of fluorine, for example, in its atmosphere, we would be highly suspicious that life might be present there, since fluorine is a very reactive gas, which does not survive for long in natural equilibrium. This concept was first put forth by James Lovelock in the context of searching for life on Mars, and was the basis for his controversial 'Gaia hypothesis'.