1. Bring along a gift of some kind. No this isn't a requirement, but just like a birthday party or another event at someoen's home it's customary to bring a small gift to the baby boy. This could be something as simple as card with a check for $18 (chai) or a small stuffed animal. I'm a huge fan of this onesie, which celebrates the naming of the child, rather than focusing on the religious aspect of the circumcision.
2. Be prepared to stay for a while. The process for a bris can range from 15 minutes to several hours. A lot depends on the arrival of the Mohel and how the baby is doing. There's usually some nosh, so grab a plate and plan to stick around for quite a bit. And on that note, be prepared to pitch in to help. These people just had a baby, and they are hosting something akin to a party. Help them out by taking care of something like the trash, the dishes, or just hiding their dirty socks under the couch.
3. Don't expect to hold the baby. This is not only a religious ritual, but it's also the first 8 days of baby's life. Do use hand sanitizer whenever it seems you might get a chance, but don't be upset if mamma wants to keep the baby near her. It can be traumatic for moms to hear their baby boys crying, so don't be concerned if she holds him close, and then when it's over usher's him back to his room for some quite time and/or nursing.
4. CELEBRATE. It can seem a bit weird to shout Mazel Tov over the cries of a baby, or seeing the tears staining the new moms' eyes, but people who hold brises and invite people to share this moment are doing so because this is a great simcha. It's a moment when they are declaring their dedication to Judaism, welcoming their son into the community of Jews and celebrating that he's come into this world. So remember to raise a toast, speak kind and exciting words, and celebrate the joyous occasion.