Ending the Section: Weave until you have about 1.25 inches done. The section from the bottom of the base wire curve to the top of the weaving you just did should equal half the diameter of the donut.
Wind the weaving wire "tail" at the base around the 18g wire curve. Use pliers to pull the wire through. Cover the whole curve and trim any extra wire. Make sure the wire end is on the inside of the curve so there's no scratchy piece sticking out. You can use chain nose pliers to secure the end. (If you ran out of wire before covering the whole curve, just spread out the loops you made.
Anytime you run out of 24g wire you will end the old wire and begin the new wire as described above. When you don't need the tail wire for your design, trim as close as possible to the inside of the base wire and tighten with pliers. Always trim AFTER the weave is secure.