It is like saying you have been on it a bit and know a bit about Facebook, but you haven't been on it long. So you are fairly new to it. In other words you are kind of new or sort of new. I hope this helps.

Yes I would tend to agree with the above answer. The usage "fairly new" basically means the same as "quite new".

It means that a person has recently started to use facebook. They may not know all the different features of the website or how to use them.