Tip #1: Do your homework.
Before you begin posting in a Facebook community, make sure to seek out the rules and review them. Administrators of online communities have the difficult task of managing the behavior of dozens, hundreds or sometimes thousands of nearly-anonymous users. You can avoid making their job more difficult by making sure that whatever you post in the group is permitted by the community rules.
It is also important that you do not post questions to the group that you have not already attempted to answer on your own. There is nothing more frustrating (especially in library-oriented communities!) than reading someone's question, only to find the answer in the first result that pops up on Google. Professional networks are wonderful for crowd-sourcing difficult questions and troubleshooting real problems, but it is a waste of everyone's time and resources if each individual doesn't do his or her homework.
Tip #2: Read carefully.
When engaging in discussions in your Facebook communities, it is really important to read carefully and make sure you understand what is being said before you reply. This is especially necessary when answering a colleague's question. Often, a poster will indicate exactly what type of information he or she needs, and what type of information he or she is not looking for. When you read too quickly and miss these statements, your responses to the discussion can easily turn out to be irrelevant and pointless, not to mention frustrating to the original poster who has to wade through useless information to find the helpful content he or she requested.
Tip #3: Don't be an echo.
Often, you will find that the comment you wished to add to a Facebook discussion has already been posted by someone else. Your initial temptation might be to repeat the same sentiment in your own words, but this is not really necessary. You can just as easily show your support for the comments you agree with by clicking "like" underneath each one. This saves other members of the group from having to read the same response over and over again, and it makes it easy for everyone to read the truly different opinions being presented.
Tip #4: Turn on notifications.
You probably don't want to be notified every time anyone posts in your Facebook communities, but sometimes you may want to get notifications for a specific post. Instead of commenting with an asterisk, period, or the word "following," you can simply turn on notifications for that specific discussion. To do so, click the drop-down menu and choose "turn on notifications." This will allow you to follow the conversation without cluttering the discussion with unnecessary comments.
Tip #5: Don't spam.
Even in communities which allow self-promotion, you should use discretion when sharing links to your own blog. It is usually fine to do this in response to requests for specific information, but it is less welcome when you post a link just to promote your blog, or to ask for general feedback. Obviously, in some communities, it is expected that you will ask for help with specific aspects of blogging, and many of these questions will require a link, but there should always be a reason behind the post, and you should also make a concerted effort to participate in the community in other ways.
These are just my top five tips - do you have others? Share them in comments!