Chatter is a great tool, and if you use Salesforce, you should be using it, and using it every day – many times a day. Chatter is great for “working out loud” and keeping others in your team up to date with what you are doing.
There is a lot of help out there about how to use chatter, including the Chatter Best Practices page on the Salesforce website and this excellent series of 9 chatter training videos created by Engineers Australia for their Chatter implementation. They may be a bit specific to just engineers and just the stand-alone chatter app, but they are very well done.
One thing I could not find enough information on is Notifications, so here is my explanation of notifications. (Well, it started out as being only about notifications, but it may now include a bit more information also).
Chatter, like most social networks, can be Push or Pull – eg you can “pull” the information towards you by going to look at your chatter feeds, or have chatter “push” the information out to you, via notifications.