One of the most important techniques to master in crochet is colour changes. Perfecting this technique is especially important when crafting amigurumi. Ideally you want to make changes without the use of slip knots or tying off of yarns.
Although I will be explaining this technique using a single crochet, the result can be achieved using any stitch. The important thing to remember is that in order to initiate a colour change you must not fully complete the stitch prior to the change.
Begin your single crochet stitch as you normally would with Colour A. Insert your hook and pull up a loop. You will now have 2 loops of Colour A on your hook. At this point you would normally yarn over to complete your single crochet but in order to switch colours, you must complete the yarn over using Colour B. Pull the new colour yarn through to complete the stitch. Your next single crochet will be continued using Colour B.
For those of you that are visual learners, Planet June has a wonderful video tutorial on completing this technique in the round for amigurumi and the Crochet Guru has a tutorial on changing colours at the end of a row.
Colour changes really are one of the simplest but most important techniques to master in the art of crochet.