Adding new yarn is most often used when you need to add another skein of the same yarn to continue a project, but it's also the same technique if you need to add a different yarn or color.
You should not tie knots when changing yarns! Just leave your ends hanging and weave them in later. The area where the tails go into the work will be loose but that's okay! You can tighten those stitches when you weave the ends in.
When adding new yarn, you want to leave a long enough tail to weave in later. We recommend 8–10". Most people wait until the project is finished before weaving in ends, but you can start as soon as a few rows after you've added the new yarn.
For the most invisible join, we recommend adding new yarns at the ends of rows, or where there is a seam. Woven in ends are usually at least a little visible so it's best to avoid leaving ends right in the middle of a project.
If you haven't already, familiarize yourself with the different styles of knitting before continuing. There are three different ways to hold your yarn when knitting and you want to make sure you're watching the right technique for you.