I think the best method is done in such a way so that you (or judges) can NOT detect where your starts and stops are, AND that your stitches are absolutely locked and will not come out. This of course is also the most time consuming way to do it.
You will begin as always by taking 1 stitch and bringing your bobbin thread to the surface, hold the tails in your left hand and begin stitching.
Now you want to separate these two threads and then tie a knot, lay that knot right tight against your work......then do it once again.....you have now knotted these threads twice, below is a close up of the first knot as it was being pulled tight.
Next you will thread a needle.........one with a larger eye and a needle threader helps or you can use a self threading needle if you prefer. (both thread tails are threaded into the eye together)
The next step is to insert your threaded needle into the quilt right where that first stitch was taken, carefully slip the needle into the batting/quilt middle only, bring it out about an inch and a half away, give it a gentle tug to cause the knots to "pop" into the quilt and then you can clip your threads closely
To do this method in areas where you have ended your stitching, you will first need to thread a needle with your bobbin thread so that you can bring it to the top....now that both threads are on top you simply repeat the knotting/threading/burying process.
and there you have it, yes it requires a little effort but your starts and stops will be secure and undetectable.
Edit: Just a note about dealing with your threads at the end of a stitch line....there is a way to do it at the machine, without threading a hand sewing needle....I do it this way but a commenter Rebecca Grace has described the process perfectly so I will use her words
Rebecca says... when you get to the ending, there IS a way to bring up the bobbin thread without using a hand needle. When you finish the line of stitching, DON'T clip threads, but just raise the presser foot and pull the quilt a few inches to the side. Then move the quilt back where it was, holding onto the loop of excess thread on the top of the quilt, lower the needle into the hole of the last stitch and bring it up again. Give a little tug on the loop of top thread, and the bobbin thread will pop up just as it does when you were starting out.
