When you are working with several colors in a row, as in pictorial crochet, there is no easy way of manipulating all the colors in your hand at once. You can hold one color in each hand and feed them through as you work your crochet pattern.
The basic method, when it comes to crochet, is simply to drop the old color and then take up the new one. However, you might find that it’s slightly quicker, in situations where you have to make several changes in a row, for example, to wrap the yarn around your little finger and just carry it across the palm of your hand.
If you use this method, it’s important that you try to keep the same tension in the yarn over the colored section as you do over the rest of the piece.
If you end up with long, loose floats on the back of your piece of crochet where you have not been able to keep an even tension as you work, you can fix this by cutting the strand in the middle and then darning it back into the work, along a few stitches, up or down a row and then back the other way.
Thimble-like devices can hold several colors at once on one finger. However, these can take some getting used to and can cause the yarns to tangle. It is like anything you are trying to learn. You just need to practice, and you will be crocheting in no time at all.