One of the most frustrating things when you're first learning how to bead is adding in new thread. Either your thread breaks, or it tangles so badly that you need to cut it or a workable length just isn't enough to finish your project.
A lot of the books don't really offer tips for adding in new thread. So now you're working out a method that will work for you. Sometimes it works out well, sometimes you wind up with a knot and more frustration.
So I'm going to explain to you how I add in new threads, and I'd love to see other beaders favorite methods. This method is for threads that can be knotted. Kevlar thread for example can't be knotted. It will cut itself.
There are a lot of methods, the one that works best for me weaves in ends as I'm working. So when I know I'm running low on thread, I weave the end of the thread through the bead work and make a few half knots at different places to anchor it securely. It helps if you go back an forth through the bead work instead of just weaving it through in a straight line. If the thread is in a straight line it's easier to pull out those half knots. Trim or zap the thread close to the beadwork.
Adding the new thread, I cut off a length that's comfortable to work with, then put on a stop bead about 5 inches from one end of the thread. A stop bead is a temporary bead that will stop the thread from pulling through the beads. Thread your needle. You pass your needle and thread through a bead, then around the bead, then back up through the bead. I have a bright red 3 mm fire polish crystal I use for this because it's easy to see against most of my beadwork, but any small bead will work. Keep the needle on the short tail.

Now, pass your needle through the last bead on your beadwork so the long end is in the right direction to continue your beading, and weave the short end through the beadwork and make a couple half knots in a few places while your doing it.
After you've woven in the short end securely, cut or zap it close to the beadwork. Slide off the stop bead and continue beading.

This method works great in peyote and netting.