Why use circular needles? It's certainly possible to spend your entire knitting career only knitting back and forth. But circular needles (double-pointed needles or DPNs are a topic for another time) vastly expand your repertoire as a knitter. You can knit a much better hat if you use circular needles! Not to mention sleeves, seamless sweaters, and more.
Many knitters (myself included) have also converted, slowly but surely, to circular needles over straights. When I have a project designed to be knit back and forth, I would say 80% of the time I use circular needles. Because the weight of the project is hanging straight down from the end of your hand, they are much kinder on your forearms. As opposed to straight needles, where the weight of the project dangles out from your hand, forcing you to lever the entire project each time you make a stitch.
When you buy a pair of circular needles (or "circs") the first thing you will notice is that the cord between the two needles is coiled tightly from its packaging. You can fix this by boiling up a pot of water. Give your cord a quick dip in the water, and the cord should relax.
The basics of starting with circular needles is easy. When you get to the end of your row, just keep going! This bit, where you first switch from the second needle around to the first, is called the "join," and there are several ways to make it. If you get stuck, don't forget to check YouTube for tutorials!
The hardcore way is to literally just keep knitting. This is the "right" way, according to most authorities. There will no doubt be a little bit of a gap there, but don't worry. When you finish your project, you can tighten it up using the tail from your cast-on edge.
My personal favorite is to cast on an extra stitch. Then when I get to the join, I k2tog the last stitch with the first stitch, and continue on.
"Join, being careful not to twist." But eventually it happens to the best of us. If you find yourself, after a few rows, knitting something that is twisted around bizarrely like a Moebius strip, then you probably twisted by mistake. There's no cure for it; you'll just have to rip back and start again.