1) Getting a vehicle is a must. You can use it as cover, to scout safely and deals some nasty damage on its own. And when you research laser weapons, the laser upgrade is terrifying (Does 120+ damage, 4/5 radius!). With it, I doubt you'll have any problems to clear small UFOs.
2) Before that a Rocketeer can fulfill the same role because you can shoot the missile down a hallway without having line of sight or worrying about missing. Just blow up the door and shoot a missile, it's far more useful than throwing grenades.
3) Spamming flares is extremely important for night missions.
4) You can choose what kind of shot you want to use with the scrolling wheel. No wonder my dudes were missing so much. (They still do, though
5) Apparently, you can install several radar domes to increase radar range instead of spamming bases all over the world. No wonder I never had enough money.
6) Similarly, you can use several planes at once to tackle UFOs and Aerial Terror sites. Very useful! I think having a lot of planes is neccessary for success since shooting down UFOs gives you money and keeps nations happy.
7) Stat grow is very important. Try not to do everything with vehicles or having your operatives killed because units improve a lot in just a couple missions.