"knitting in the round" is what you do to knit socks, or hats or any garment which can be thought of as a tube (even sweaters and their sleeves can be thought of as a series of tubes all joined up). When you knit in the round, you need either:
1) a set of 5 or so double point needles (whatever pattern you are using will specify the size and number of double pointed needles that you will need);
2) one or more circular needles (again your pattern will give you details).
Here's a cool webpage with basic info about knitting in the round:
There is also a great webpage about learning how to knit socks which shows you how to start a sock with double pointed needles. It's here:
The pictures and instructions show how to start knitting a basic tube on double pointed needles. The pictures will give you a great idea of the concept of what you have to do.
But you could make a simple hat as a first project using this method....I think Amy has some free patterns on this site!