One way to secure your beginning and ending stitches is with tiny locking stitches. Use the needle up/down feature to place several stitches very close together before engaging your stitch regulator. Try to put 10-15 stitches within 1/4-inch for best results.
If you want to compete in quilt shows, or are looking for a way to hide threads that begin in open spaces, then try burying your thread tails. Hand quilters have buried their threads for decades, and several methods exist to accomplish the same task. In the following video I demonstrate just one way to bury your threads…you may find others that work for you, too!