Picots are just spaces between stitches. A short length of thread is left before you start the next stitch and when that next stitch is done and slid up next to the other stitches the thread forms a picot.
I have tatting demos on my web site that have taught a lot of people how to tat. Here's the address for the demos
Sharon's Tatting Demos I suggest that you start with chains using 2 colours of contrasting thread as it wil give you the best oportunity to see what's happening. I have had a lot of people get stuck because they thought the were flipping the stitches, but they weren't. Larks head knots can look like a proper doublestitch but the rings close from the wrong end leaving spaces between the rings. If you start with chains then you'll know for sure that you are making the stitches correctly.