How could we find alien life?
There are many ways to search for alien life and some of them are being attempted right now. Here are some examples:
Exploring space
We can send robotic rovers, and eventually people, to other planets and moons to look for signs of life. This could provide definitive proof, but it is limited to the places we can physically reach. For the foreseeable future, we’re stuck inside our own Solar System, which is very limiting indeed.
Looking and listening for ET signals
We can monitor the skies listening for radio signals and looking for signs such as flashing lights. Again, this could provide definitive proof but only if the aliens happen to be sending out signals that we can detect. You can even help in this quest yourself with the SETI@home citizen science project.
Analysing distant atmospheres
We can use remote sensing equipment to determine the composition of atmospheres on other planets. This could reveal "biomarkers", or evidence of living organisms. For example, a high level of oxygen or a thick ozone layer would be evidence of biology on the planet. This technique is difficult but the latest telescopes currently being built will be sensitive enough to do it.
Wait and hope
The easiest way to prove the existence of aliens would be to have them visit us, but of course this plan is not exactly pro-active.
Scientists have examined claims that Earth has already been visited by aliens but have not been able to substantiate any of these claims.