For capturing Aliens alive your best bet is to wait until just one is left. Then suppress him, and soften him up with a Pistol shot. Then make sure your Arc Thrower guy runs right next to him to get flanking so it wont miss.
You should be going for captures as soon as you can. Don't put your squad in danger to capture a live alien, but if you get down to what you feel is the last guy, move everyone in and go for it. Interrogations often lead to new research and sometimes outright new tech that you can start making immediately.
It's will be a fully colored shield icon instead of a half colored shield. If it's yellow that means an Alien would get flanking bonus against you there I think. Either kill it or move somewhere else if that happens.
For Large UFOs (when they guy says we will need to send our best equipped ships) you can take them down with 3 un-upgraded default ships if you dont have any good ships yet such as in fairly early in the game.
I lost two and the third one took it down, but I made up for the lost craft with everything I found in the UFO, not too good of a tip maybe but oh well lol.