You probably have the correct type of yarn, but the 5mm needle is a size 8, the 10.5 is 6.5mm, so the one you have is smaller than in the pattern. It sounds like you'll be knitting a blanket that's knit on the diagonal, so using the size 8 may be okay, or it may be too dense a knit. I'd get the larger needle myself, but you might knit looser. (see more info below)
You start at a corner with the 4 sts, then you kfb in the first st of every row. That will increase your sts and it's done by knitting in both the front and back `legs' of the stitch. That's how you go from 4 sts to begin with to 208 all on the needle. If you got straight needles, this is going to be difficult to fit them all on which is why the pattern suggests circular ones. You can knit with them like straight ones, but they hold a whole lot more sts, so if the size 8 you bought isn't circular, you may really want to get the other size needles. For understanding how to do the kfb, go to the Increase section - http://www.knittinghelp.com/knitting...s/increase.php
It's also called the Bar increase.