Nothing special. Label side up, push it in the slot most of the way and it gets sucked in.
Try different discs first--maybe you've got a damaged (or copy-protected) one.
It is also just possible, I think, for that kind of behavior to be caused by a software glitch rather than anything physical: I once had a bad DVD that didn't want to eject, and when it finally popped out (I just had to wait), the computer wouldn't accept other discs, just like you describe. It was like the DVD drive took a long time before realizing the old disc was gone and it could take a new one. I don't remember if I powered off and back on (you could try that), or if it just resolved itself when I waited (which OS X glitches have a tendency to do).
But you may well have a physical problem like some debris stuck inside, or a bad (scratched?) disc, or a bad optical drive. If you live near an Apple Store that's easy to check at the Genius Bar. If not, Apple will probably send you a shipping box (or you can carry it to the nearest repair location listed online) if they can't help you solve it on your own.
Related note: there IS a "trick" to ejecting. You have to HOLD the eject key down for a moment (quarter second) or it won't eject. That's a safety feature so the disc doesn't eject accidentally if you quickly hit Eject instead of Delete. (Or, just drag the disc to the trach/eject icon, or click it and choose Eject, Command-E.)
Good luck.