Start by holding a "starter square stitch", like this...

Take the strand NEAREST YOU and take it UP, OVER, and ACROSS the small checkerboard to create the first loop. Note how we CROSS the starter stitch, UNLIKE the Square Stitch!

Now take the strand farthest from you and bring it UP, OVER, and ACROSS the starter stitch, so that its loop sits NEXT TO the first loop you made. Again, note how it CROSSES the starter stitch.

The first WEAVE does the same CROSSING. Take the strand on your left UP and OVER the nearest loop, then CROSS and UNDER the second loop. Be VERY careful here. EVERY strand needs to CROSS in this stitch, or else it will fall apart on you.

The strand on your right comes UP and OVER the loop nearest it, then CROSSES and goes UNDER the farther loop. It crosses the earlier stitch, NOT the strand you were last working with. It should sit ASIDE that strand...

...and should look similar to this before we pull the strands tight...

...and should look like this after we pull all strands tight.

Let's do one more stitch, so we're straight! Take the first strand UP, OVER, and ACROSS the previous stitch to form the first loop...

...then take the opposite strand UP, OVER, and ACROSS to form the second loop, which should be sitting right beside the first loop. Do NOT cross the loops!

The strand on your left comes UP and OVER the loop nearest it, then CROSSES the center and goes UNDER the second loop...

...while the right strand comes UP and OVER its nearest loop, then CROSSES and goes UNDER the farthest loop, again sitting ASIDE the strand you were last working with!

Check the placement of your strands while they're still loose...

...then pull them all tight to complete the stitch!

Here's what our Circle Stitch looks like after we've completed numerous stitches...

...and here's the Completion Stitch, right before we pull all central strands tight!

A Circle Stitch Project, properly completed!