Summarize the following:
Make the final stitch in your row, just as you normally would before starting extra chain stitches to turn around and move on to the next. Cut the yarn about 4-6" from where it comes off the piece you are working on. This extra thread is called the tail. You should have one loop on your hook at this point. Now, catch the yarn on your hook and pull it towards the loop as if you were going to make another chain. Now, instead of creating a loop with the yarn, pull the thread all the way through the loop. Give the tail a firm pull. You should see the loops behind and around it tighten up until it looks like your piece ends in a knot. Technically you are done, though you should not generally stop here as this connection can come undone. Take your tail and weave it back through the stitches that you have made. This will hide the tail and keep it from unraveling the knot you just made. Now, there are LOTS of different theories on the best way to weave the yarn through the piece. Some people use a yarn needle, others use the crochet hook, some people weave the thread back and forth through the first and/or second rows, some people pull it in a single line through the middle of the first row. Experiment and find a way that you like but most methods likely work equally well.
Make your last stitch. Cut some extra thread. Start as if making a single crochet chain. Pull the thread all the way through. Tug to secure the knot. Weave in the ends.