To shoot down a UFO you will need a satellite and at least one interceptor. Once a satellite has detected a UFO via scanning the geoscope in mission control, you need to launch an interceptor in the hope of bringing it down. In the beginning of the game this will be fairly easy but as the game progresses, you will need to upgrade not only your interceptors themselves but also their payload to be able to take out the alien’s larger UFOs.
A good strategy is to hanger at least one interceptor per continent with a satellite in orbit. On average you will encounter 1 or 2 UFOs per month so unless you hold off progressing the story, this will take you several playthroughs.
Save at the Geoscape then ignore everything & only shoot down UFOs. At game over just reload your save & do it again.