This website may have been written when the new Pages system and layouts were first launched, but it’s still very valid and useful.
It contacts all the information about the picture sizes you need, and a few extra helpful tips besides.
Do bear in mind though, even though your Facebook Page’s profile picture needs to be 180 pixels square, Facebook actually automatically crops out 10 pixels on all four sides. So basically, create an image that’s 180px, but know that you’ll lose a bit around the edges.
Of course, you can also have me do this for you, I make a lot of these for people! In fact, I’ve done over 100 in the past 12 months.