The traditional method to start a new row or round in a new colour, is to slip-stitch the new colour to the previous row and start with a few chains. Unfortunately, the chains are not very neat. I use standing stitches instead.
In these videos, I demonstrate the standing double crochet (US terms), the standing half double crochet and the standing single crochet. Use the first video if you are a right-handed hooker and the second video if you are a left-handed hooker.