Follow what you can in the conversation - Whether it is focusing on everyone's answer for a few questions or following a few responses for all the questions, follow what you can handle.
Have the right tools - There are a few different ways to get started technology wise for your Twitter chat. Check out my post outlining a few options.
Lurk once, participate after - A new group may be intimidating for you. That's okay! "Lurk" or watch the chat occur the first time, and get involved in the chats after that first one. Get a feel for how people respond.
Don't forget the hashtag! - This probably should be the first one, but don't forget to include the hashtag in your tweet! It is important so you can add your thoughts to the pool and continue the discussion with everyone. It can be first or last or somewhere in the middle of your tweet.
Check Out the archive - Whether it is you manually searching the hashtag after the chat or catching a archive someone in the chat made, take a look at what was said. There is a lot going on and everyone is talking at once. Chances are, you missed an important piece of information or thoughts that you either love or want to know more
Network - Maybe easier said than done for some people, but connect with others in the chat, ask questions, continue the discussions after the chat and days in between the chats.
Introduce yourself - Even if all you are doing is lurking, be sure to introduce yourself to the group. Goes along with the networking.
Find the MOD - It is important to find the moderator or MOD of the conversation. Sometimes it is a person and sometimes it is an account for the chat. It is important to know who it is so you can find the questions easier while you are chatting.
Have fun! - This is a neat feature to help you continue to learn and grow as a professional while sharing your thoughts. Plus you get to spend sometime with people interested in the same thing as you, which is always awesome!