The first time a supply ship lands (disappears from the map), just take note of the place where is disappeared because it will be building an alien base there. Don't bother sending an aircraft to patrol there as you cannot find the base yet (and also you can never find landed supply ships). Instead, build a SAM site exactly where it disappeared.
After a few days (3 days?) the supply ship will have finished building the base and will take off again, and hopefully your SAM site will shoot it because there will be no notification that it has been re-detected and you will get no mission button in the top left of the geoscape and the game will not pause so you will miss it without a SAM site.
You can only detect an alien base when the second (or later) supply ship lands there.
When you see another supply ship, send a firebird or some slow aircraft to follow it. You have to keep clicking to reposition your aircraft since it has no follow mode unlike XCOM aircraft. If the new supply ship heads towards where the first one built the base, then you are in luck and it is not building another new base but just supplying the first base. Follow it there with your aircraft and turn off the autofire in your SAM site so it does not shoot down the supply ship. Once it disappears, send your aircraft to patrol on the exact place where it disappeared, and in a while the alien base will appear and you can attack it if you want (so you can fill your aircraft with soldiers so you can land right away).
The more times an alien base gets supplied, the bigger it grows so if you are not ready to attack it, leave the SAM site on to shoot down supply ships before they land there to make it bigger.
Alien bases are big so if you have a Hercules heavy lifter drop ship that can carry 12 soldiers, that will be useful. You need a lot of troops to move down the different corridors to clear the whole place. Troops should all have medikits and move in pairs so they can heal each other if they get shot. Once you win you get an alien psi device to research but nothing useful comes from that.
The biggest UFO that i have seen is the bomber. Are there any other types after that?