If you're knitting the perfect piece
but need to change from one ball of wool to another without leaving
end bits to clean up afterwards, you can felt two ends together. It
works well with two ends the same colour, and doesn't look too weird
with different colours.
This method only works on wool and other animal-derived yarns, it won't work with cotton or acrylics.
1. Take your two ends of wool and fray 2cm (1 inch) or so.
2. Dip each end in a glass of water.
3. Weave the ends together a little bit.
4. With dry hands, rub the two ends together between the heels of your hands. Do so very briskly, so that your hands get hot. The heat will dry the ends of the wool, and the water will felt the two ends together.
5. Pull the wool from both directions a little bit to check the strength. It should be as strong as the rest of the wool.