In most cases, Facebook does a fantastic job streaming live audio and video to your computer, however, sometimes there are problems. Here's a list of things you can do to insure your internet connection will work fast enough.
1. Disconnect anything that hogs up your wireless internet signal; Other computers, iPads, phones, Wii, Netflix, Video Game Consoles, Streaming TV, Etc. This will insure your computer gets the maximum bandwidth to work with.
2. Plug directly into your internet router. This will insure that your getting the absolute fastest internet available.
3. If you are using a wireless router, make sure you are within a strong range of the router - A weak router signal reduces bandwidth significantly and will effect the quality of the session. *this is the most common problem I see.