There are many, many chats on Twitter for people to participate in. They are found by knowing what the hashtag for the chat is. For example, I know on Tuesday evenings, there is an #smmanners chat. It’s a discussion of Social Media manners. Chats are awesome because you can learn a lot from people you may not interact with.
So, once you know what the hashtag is, you can search the hashtag and jump in. What I prefer, though, is to go to http://www.oneqube.com/, which is the new alternative to the non-defunct (or soon to be), tweetchat.com . You log in with Twitter, enter the hashtag of the chat, and see what everyone is saying. Every tweet you send out while using http://www.oneqube.com/ will automatically include the hashtag.
If you use Tweetdeck (not sure how other third-party apps work), you can add a column with the hashtag.
Always remember (except for when you use tweetchat.com) to add the hashtag into your tweet for others to see.