Some directions/tips: Both of the vine-twigs I used were cut from a weedy shrub that lives near my house.
For the criss-crossy web one, I carefully bent the twig into a circle, then tied an end of a ball of white yarn around the overlapping twig ends. I wrapped the yarn around the overlapping sections of the twig (that's the wrapped section you see above), then tied it off. Then I wound the yarn around the circle at random. When it seemed fairly full, I tied it off. Then I tied a knot of green yarn at the intersections of the criss-crossed white yarn. I trimmed the ends of the knot very short.
For the woven circle one, I bent the twig into a circle and just tied the ends together with one loop of white yarn. I tied the other end of the yarn to the opposite side of the circle, and then I did the same thing three more times, creating what looked like the spokes of a wheel. The problem with having an even number of spokes is that your weaving doesn't naturally alternate between over and under; it ends up like a god's eye, if you can imagine what I mean. If I did this again, I would tie a piece of yarn around the center of the spokes, and tie its other end to the twig circle, thereby creating an odd number of spokes. As it is, I had to skip a spoke each round in order to make it be a true weaving, and it was tricky to make it look neat. Anyway: Once you have your spokes, tie your weaving-yarn to the center, then start weaving around the spokes, spiraling out from the center. To change colors, just tie the new yarn to the end of the old yarn. If you use pleasingly-plush yarn, the knot is easy to hide with a poke.
So there they are! Happy winter solstice!