How Do We Look for Life on Other Planets?
There are, as best we can estimate, hundreds of billions of galaxies in the universe. (There may be more.) Average galaxies carry the weight of hundreds of billions of stars. If a habitable planet whirls around just one star in every million, the number of worlds which could harbor life would number in the quadrillions. (Roughly 10^16, i.e. unfathomably many.)
Does this suggest that our skies should be clogged with UFOs so numerous that no government could hope to cover them up? Not necessarily. Limited to traveling at speeds less than that of light, it would take thousands of years for most of these visitors to reach earth. Millions of years would be required for those outside of the Milky Way. (Of course, this time could be cut way down if an advanced alien life form figured out how to travel via wormholes, but this is science fiction as far as we know.)
Our most distant spacecraft, the Voyager I probe, has spent half of a lifetime traveling into the void, but it has only just left our solar system. It will take 74,000 years to reach the distance of the nearest star.
So, unless future physics reveals superluminal travel, the vast distances between stars and galaxies limit our chances of directly meeting aliens. Distant civilizations may launch a different type of traveler out into space to meet us, either intentionally or unintentionally: Electromagnetic waves. These waves live forever and can't be cloaked from our eyes and ears.
In contrast to our space probes plodding along at 38,000 miles per hour, the radio waves we've beamed into space for over a century have been traveling at the speed of light. A short calculation based on local stellar density of 0.006 stars per cubic light year reveals that our radio broadcasts and television transmissions, from famous speeches to toothbrush advertisements, have now reached approximately 25,000 other stars.
We might then have better luck looking for electromagnetic wave signals from extraterrestrial life than actual (grey) flesh and (green) blooded aliens. What sort of waves are we looking for, and where do they come from?
Radio waves are the most obvious candidate.
While other civilizations could be beaming "HELLO" to us across the vacuum (we've done this ourselves), more likely we might capture transmissions not meant for us. If their atmosphere is similar to ours, they may be communicating on-planet in a way much like we do: AM radio broadcasts (waves roughly 1/3 to 1/10 of a mile long), FM broadcasts (10 foot waves), as well as VHF and UHF television (30 feet to 3 feet, and 4 inches to 3 feet, respectively). All radio waves from roughly a fraction of an inch to many miles long can be used to transmit information through an atmosphere like ours, and they also penetrate through it and into space easily.
Even better, these signals can come in from space, penetrate our atmosphere and hit the earth's surface. Enormous radio telescopes here on the ground, including the massive Arecibo telescope and the NRAO array are frequently used to listen for signals coming from space that don't seem natural.
Arecibo telescope (public domain)
There is bad news, however: we've been doing this for years, but we've only seen one anomaly that never reoccurred. What else can we try?
When NASA wants to communicate with the moon, they use lasers. Not that anyone on the moon is talking back, but retroreflectors left on the moon's surface by Apollo astronauts reflect the laser signals and return them. (This allows the distance of the moon to be found correctly to within two one-hundredths of an inch!) If there were a permanent human colony on another planet or moon, laser signals would be a great way to communicate.
We can look for laser communication between alien worlds as well. At just the right time, two communicating planets could be lined up with us just correctly for the laser light that misses the target planet to shoot straight through space and reach us. This light mostly penetrates our atmosphere and could be seen by ground-based optical telescopes. A precise planetary alignment and laser detection would require an incredible amount of luck, but SETI (Search for Extraterrestrial Intelligence) workers have been trying.
There is a more speculative approach still, bordering on science fiction.
Genius physicist Freeman Dyson first suggested the idea of a civilization becoming so energy-hungry that it needs to yoke the entire power output of the star about which it originates. Building an enormous "Dyson sphere," or a blanket of small orbiting patches surrounding a star that absorb nearly all of the star's light would be the logical method for doing this. The sphere or blanket would absorb visible light, but likely leak lots of infrared electromagnetic waves. Astronomers are actually combing through telescope data looking for areas of galaxies which generate abnormally high amounts of infrared radiation, possibly indicating the presence of these spheres. The odds may be slim, but it's still a lead.
Whether these searches amount to science -- or just speculation -- is up for debate. Nearly all funding for SETI work is privately financed via donation, so if nothing is discovered, little public money has been lost. Eventually one of these long-shots may pan out. What an incredible discovery that would be.