Welcome to Knitting Help!
It always helps to have pattern names and links when asking questions. What it sounds like though is that you're making the blanket diagonally. It also says to increase "in" first stitch so I would do a KFB (knit front and back)- instructions are in the video section linked above. Once you get a bunch of rows you'll see how the pattern works.
As for the circular needle..that is because as you increase you'll be getting more and more stitches and it's much, much easier to have them on the cable. You couldn't easily make a blanket in one piece on straights. To use them just turn your work like you always do. The only difference is your other needle is attached.