Hook your 360's AV and power cable in and plug the RF board (the circuit board that has the Ring of Light LEDs) back into the 360. Otherwise you won't be turning it on. :D
Turn it on without the fans plugged in, checking to see how fast the heatsinks heat up. Getting hot in less than a minute is excellent. Now plug in the fans and put on that plastic fan shroud. Turn it on again and it should boot up normally, assuming you did the heat test (if you didn't plug in the DVD drive, the center LED will blink green).
If it goes RRoD instead, unplug the power cable, re-insert it and try again. If you cannot get the console to boot, press down on both the heatsinks with even force and power it on again. If it boots, power it on with only one heatsink pressed upon. If it boots with that particular heatsink pressed on, power the 360 off and keep re-booting until you find the problem corner(s) on the heatsink that needs tightening.
The idea is to tighten any heatsink corners that aren't tight enough in order to allow a good connection for that processor.
So if it boots up normally and you can play a game for at least an hour without it locking up, you've worked your magic and the 360 can be re-assembled! Have a beer, rent a movie, eat some gummy bears, do whatever it is you do to treat yourself because YOU DID IT!
The next step goes over some measures you can take to prevent overheating.