The only time I use double-pointed needles is when I am decreasing a hat and the project no longer fits well on circular needles--although, you can use them in place of circular needles for most projects.
The first time I used them, I just bought them because the pattern I was using instructed me to switch from the circular needles to double-pointed needles. I have to admit, when I first tried to use them, I had no idea what I was doing. I tried to knit several stitches, then pass each one over to the next needle one at a time. I kept moving the needles around and around, but it took me forever! It was definitely one of my most ditsy crafting moments ever. To save you from similar humiliation, here are some simple steps to using double-pointed needles.
Basically, what you are doing, is knitting one double-pointed needle into the project, and knitting another needle out. When switching from circular to double-pointed needles, you begin by taking a double-pointed needle in your right hand (as in my previous knitting posts, I assume you are right-handed and knit like I do). You knit stitches onto the double-pointed needle. I usually split my project into thirds or fourths to determine the number of stitches that should occupy each needle.
I will be linking this up to these link parties.