Start with X-Com: UFO Defense (the first one). See if you can get 'gold', the windows version. If it looks corrupt, there's a fix out there, but most versions you will find are fixed.
You start playing by making a base (it starts you on that screen), put it somewhere in the middle of north america or central-west europe or something.
Now, you can poke around your base and look at the shiny buttons, or wait for a UFO to pop-up. First thing you want to do is go into your base, research button, and start researching medikits with all 50 researchers. (Later, once that's done, you'll put all your engineers that will fit on building medkits.) But mostly wait. After starting research, put time up to 1hour or something, time will skip by fast.
Within a day or a couple weeks, your radar will pick up a UFO. Set time to 5s from the menu it gives you, and send an interceptor after it to shoot it down. Once you're in range, set aggressive mode (closes in faster). If you shot it down over land, dispatch your skyranger to the white crash site. (If it landed before you shot it, dispatch your skyranger to the green landing site!)
Now shoot aliens. You'll die a lot. Save at the start of tactical. You'll get the hang of it soon enough. Congrats, you downed your first alien ship, and captured some loot. If you research an alien plasma pistol and an alien plasma pistol clip, you can use that gun...and it will beat the hell out of your first weapons.