Use the buttons that reserve TUs for reactions, move in groups of 2-3, groups should back each other up.
Always smoke grenade right out front of your
skyranger so they can't see you deploy.
You don't have to win every mission! just landing and taking off gets you points. Especially if the game throws you something like an ethereal terror mission early on (guys in brown cloaks) just say fuck it and leave. Your soldiers are way more important than that country's funding.
Try to get PSI before you start getting blasted by it. You have to capture a Sectoid leader and research him, though you should research another captive alien first so you don't just get Alien Origins.
If you knock a ship down, the only reason to start a mission on the crash is if you want something from it. Their mission failed. Concentrate on the landed UFOs instead, so you can stop them from getting points (and you get way more booty from it).
Alien bases—just find the command center and get everyone in there facing the lift. You might have to blow up the purple tables too, I forget. Anyways they'll come to you after that (also this is a good opportunity to capture a commander, which is rare).
Getting the hyperwave decoder early on by capturing a navigator is really useful too.
Also there are ways of making money through manufacture if you want to know them.
Basically just be careful and take out the enemy in missions the way a team would
IRL. Make sure everyone's supported and take it slow. you'll still lose dudes all the time in terror missions but that's just how things go down.
Also if you're up against
Chryssalids one option is to make everyone hold a prime 0 grenade. If they get hit, they'll immediately drop the grenade and it should at least kill the original Chryssalid (they're weak to explosives).
And actually do research medkits and take a few they're goddamned useful.