How do you change a skein of yarn when you finish the other while knitting?

There are a few ways.

One is, if the yarn is wool, to wet both the old and new ends and weave them together a little bit, and then rub them together very vigorously. The heat and agitation should felt them together. Tug them apart a little to see if it's sturdy before you continue to knit.

If the yarns are the same colour, or you don't mind it looking a bit strange, knit with both yarns together for five or so stitches and then drop the end of the old yarn.

If you want it to look very neat and the colours are different, use a slip knot to tie the two yarns together and knit normally. Later, go back and undo the slip knot and use a large needle to stitch the ends into the work securely and invisibly.