Step one: Get the first regeneration upgrade.
Step two: Get the blade launcher maxed out.
Step three: Max out rail gun.
Step four: Max out grenade launcher.
Step Five: Win!
That's all there is too it. Even on the hardest difficulty, it's a piece of cake after you get regeneration and max out the blade launcher. The rail gun is perfect for the later levels, because of its ability to kill many greys at once. The level 4 grenade launcher is the most powerful weapon you'll use against bosses, until you get nukes, of course.
P.S. Level 3 Regeneration is exactly the same as Level 2. Wait until you can go directly to Level 4.
P.P.S. Go nuke some greys! :wink:

Haha! I'm now the Supreme Commander of X-COM. Time to kiss Earth goodbye.
My first order of business: Homeless people make cheap rookies, and are great at opening UFO doors. Heck, they're so cheap, I'm going to replace all personel with them!
Secondly: This organisation takes too much money to run. Weapon shipments will come from Siberia from now on. Costly maintenance is to be cut on all facilities. That includes venting.
Thirdly: We have a new colonel. His name is Facehugger, he loves aliens, and I want you all to treat him with respect.
Lastly: I'll be in my condo on an undisclosed island, if you need me. Good day.
FMIX-The General Stores