What's the correct method for putting pegs back in?

Generally, the pegs have a slot in them, for the string to go in, like these:

I see the slot, the string is in it, it's just that the peg doesn't go firmly back into the hole all the way. It might be able too, I'm just afraid to push very hard. I'm already pushing pretty hard as it is, I don't want to break anything.

It may be that you are ot pushing the string in far enough.

You need to bend the string (to about 45°, about 1 cm away from the ball end. Psuh the string into the hole so that the bend is facing forward and the ball is no longer visible in the hole. The bridge pin should slip over the string without any problem, assuming it is running in the slot. Now, holding the pin in place with one hand, pull the string with the other - you'll feel the ball come up against the bottom of the pin, at which point the pin should remain in the hole.

That's it.

Thanks greybeard, that seemed to do it. When I pulled the string while pushing the pin it clicked into place.

This has probably been posted before, but here's a great site for info on string changes and other guitar stuff:

http://www.frets.com/FRETSPages/Musician/Guitar/Setup/SteelStrings/Stringing/ststringing1.html

I don't like using pliers to remove the pins. I prefer using the notch on a string winder, as shown here:

http://www.frets.com/FRETSPages/Musician/Guitar/Setup/SteelStrings/PullPin/pullpin.html

This nine pound hammer,
It's a little too heavy...

Thanks greybeard, that seemed to do it. When I pulled the string while pushing the pin it clicked into place.

I love it when a plan comes together. :D