Instructions
Bring your new rabbit, in his cage, over to your pet rabbit. Set their cages next to each other for the first day. This will give them time to hop over, look at and smell each other through the cage walls, while still keeping them safely separated.
Put the cages in a spot where they can roam free (like a blocked off kitchen), and open the cage of your old rabbit. Let him come out and hop around and check out the new rabbit through her cage. Then put him back, and let your new rabbit do the same thing to the old rabbit.
Leave both cages open, and let the rabbits come and go as they please. You want to set up a litter box on the floor, since they will enjoy jumping in and out of that in their excitement when they first meet. Sometimes you can leave the cage doors open and they won't come out at all, so you might have to take them out and see what they do.
Let the rabbits chase each other around. There may be some nervous corralling by the dominant rabbit, or one rabbit may mount the other rabbit (known as the "bunny handshake.") This is just them getting to know each other. If they fight at all, try lifting one of the rabbits out of the away by the scruff of its neck, or gently squirting them both with a squirt gun.
After a few getting-to-know-you sessions in your kitchen, when they seem calm and happy with each other, you can let them room together in the same cage. This is a wonderful thing, to see two rabbits snuggle. Once they are friends, they are friends for life.
How to Introduce a Pet Rabbit to a New Rabbit
You're doing the greatest thing. You have one rabbit at home, and you've decided to get your pet rabbit a new friend. The best idea is to get the opposite gender of the rabbit you have currently, since boy and girl rabbit couples seem to get along the best. Two girls get along well, too, and two boys can learn to like each other, but they will sometimes fight. Once you have that new rabbit, and you're bringing it in to meet your current rabbit, you want to introduce them gradually to keep the potential fighting at a minimum. You might want to have a squirt gun ready to break up any fights!