For peyote stitch and brick stitch, you can change your thread path by passing your needle down through a bead that is next to or alongside the bead you are coming out of. Then continue to weave through the beadwork, paying close attention to the tension of your thread. Remember to pull the thread through each bead one at a time, but do not pull tight.
You can change directions several times, and tie a few half-hitch knots in between the threads for added security.