There are lots of tutorials on the web that show you how to crochet a flat circle, working in joined rounds or in spirals. The problems I have with these tutorials is that they're either too vague ("keep adding stitches on each round" - how many, how often?) or too rigid, requiring careful counting that's hard to follow, especially on spiral work where it's hard to keep track of what round you're working on. When I'm designing my own project, I want to be able to pick up the work and just go, without a lot of confusing counting and fiddling with stitch markers.
Through experience, I have learned that my stitches will tell me when it's time to increase. Once you can read your stitches, you never have to count again to make your own free-handed flat circles. (If you're following someone else's pattern, you'll still want to match their directions, of course, to make sure the stitch count comes out right.)
So, here's what single and double crochet stitches look like, worked in straight rows. I show this as a base comparison:
I know, the single crochet doesn't look like a straight row, but that's just because I wasn't careful enough laying the piece out for the photograph.
Here's what the same stitches look like worked in a flat round, between two increases. See how the single crochet stitch looks like a V at the bottom, and the double crochet stands up straight?
And here are the stitches telling me it's time to increase. See how the left arm of the V in the single crochet is straight up now, and the double crochet visibly leans to the right? If you're working left handed, your stitches will lean toward the left, instead.
When you see that lean, add another stitch in the same place.
Then continue on, placing one stitch in each stitch of the previous round until you see the lean again.
That's it, no more counting stitches to keep your work flat, and no more frogging to fix unwanted curling or cupping. If you need to end up with a certain number of stitches (say, to add a shell stitch edging, or somesuch) just count up how many stitches around you have at the moment, figure out how many more you need, and stop stitching when you've added enough increases to get to that number.
Everybody gets hot pads for Christmas! :D