Knitting on circular needles is very easy. If you don't join the ends, you can use your circular needle to knit flat pieces, just like you'd knit on conventional needles. Because of the long connector between the needles, you can knit large items like afghans and not have to join then.
You can also knit in the round on your circular needles. When you do, you'll find that the right side of the work is facing towards you, which can make patterns easy to see.
You cast on to your circular needle in exactly the same way that you cast onto straight needles.
Continue to cast on until you have the number of stitches required for your pattern. You'll find that the circular needle is now full. It is extremely important when joining you work that it is not twisted around the needle! If your piece is twisted, you will end up having to rip it out. To join, hold your needle so that the yarn is coming from the right. When you are knitting in the round, it is a good idea to use a stitch marker to know where your piece began -- slip one onto your needle now if you will be using one.
Place your knitting on a flat surface and carefully turn your cast-on stitches so that they are all facing in the same way (in our example, they are facing to the bottom and inside of the needle.)
Then insert the right needle into the first stitch that you cast on and knit the stitch. Be sure to pull the first stitches tight so you don't get a gap where the rounds join.
Continue to knit -- you'll find that the 'right' side is always on the outside and that, as your work grows, that patterns are easy to see!