Circular needles are the most common type of needles today, because they allow you to do so much! The simplest being that you can knit in the round. This allows you to make things like hats and sweaters without having to seam.
To work in the round, cast on as many stitches as your pattern says (or however many you want if you're winging it) and make sure they fit all the way across the circular needles you're using.
Then, and this is very important, make sure your cast on stitches aren't twisted around your needle so that when you join you aren't making any twists in your work! The yarn should be coming from the right needle before you join. It's also a good idea here to place a marker on the right needle so you can easily tell where the beginning of your round is.
Then knit (or purl, depending on what your pattern says to do) the first stitch on the left needle using the yarn attached to the right needle. Viola! You've joined to work in the round! Watch the videos below to see it all in action.
If you haven't already, familiarize yourself with the different styles of knitting before continuing. There are three different ways to hold your yarn when knitting and you want to make sure you're watching the right technique for you.