There are 2 kinds of circles you can make: circles with joined rows, or circles worked in the round.

what you can make with them:

Coasters, placemats, doilies, floor mats, rugs, potholders

how to do it:

Here are charts detailing how to make a circle with different kinds of stitches.  If you’re making a circle with joined rows/rounds, you’ll need the turning chain chart, but if you’re working in the round you can ignore this.

Ch4 if working with sc or hdc, ch6 if working with dc or tr, and ss in first ch OR make magic ring, ch1.
Row 1: If you want to make a circle with sc, you will need to start with 6 sc in the ring/circle; hdc will start with 8 hdc; dc will start with 12 dc; and tr will start with 18 tr.  ss in first st to finish row and make turning chains if you are joining your rows; place marker (PM) if you are working in the round and begin row 2 without turning chains.
Row 2: Work 2 sts into each st of row 1.  ss in first st if making a joined row circle, PM if working in the round.  For sc circles you’ll end with 12 sts; hdc will end with 16 sts; dc will end with 24 sts; tr will end with 36 sts.
Row 3: Work 2 sts into every other st of row 2.  ss in first st if making a joined row circle, PM if working in the round.  For sc circles you’ll end with 18 sts; hdc will end with 24 sts; dc will end with 36 sts; tr will end with 54 sts.
Row 4: Work 2 sts into every 3rd st of row 3.  ss in first st if making a joined row circle, PM if working in the round.  For sc circles you’ll end with 24 sts; hdc will end with 32 sts; dc will end with 48 sts; tr will end with 72 sts.
Row 5: Work 2 sts into every 4th st of row 4.

See the pattern?  Continue in this way until your circle is as big as you want it.  If working with rounds, tie off and sew in ends.  If working in the round, finish round and ss in first st of next round, then tie off and sew in ends.

If your circle starts looking like it has edges, there’s an easy fix: just shift the increases in a row over a few stitches from where the pattern says they should go.  Keep the required amount of inc per row (6 for sc, 8 for hdc, 12 for dc, 18 for tr), just do them between the incs in the previous row instead of right on top of them.