The trick is patience, I hate it when I have to change this type of halogen bulb. First of all, if you have handled the bulb with your bare fingers wipe off the skin oils as their presence will make the bulb burn out or pop very quickly.
You can use a cloth, rubber or latex type glove. The gloves make it easier to handle the bulb. It is a matter of getting the prongs lined up with the sockets or holes. Looking at the socket and seeing how and where the holes are is helpful. Then try putting the bulb in to match the holes. If they aren't lined up move the bulb slightly, back and forth, with light pressure until you feel the openings and then press bulb in until it stops. Do this in the morning when you are fresh. Good luck.