If it is a small area you can carry the colour along the back, but you have to make sure you keep this ‘float’ loose enough so that it doesnt pucker your yarn. That meens when you get to the place you need to change colours, you drop one colour and pick up the new strand, so that it comes from under the old colour so they are crosed, this links them together nice and tight. knit across the stitches in this new colour. When you get to the spot you need to change to your first colour then you simply pick it up, making sure the strang goes right acros whenre you have just worked, but not to tightly, cross the yarns over like you did before and start knitting with the yarn. This is called stranding because you have strands across the back.
The other option is to have several small balls of yarn. Have a ball for your main colour and then a separate bobbin with the other colours on hanging down the back waiting for you to get to them. When you get to the new colour you cross the yarn over/twist them to lock them togehter and start knitting, then drop it at the end. You will have tails to weave in for each colour, but would only have to weave in the tails at the end of the pattern, rather than every row which is nice. This is the methid known as intarsia.