Probably the most difficult thing for people new to intarsia knitting is keeping all the different strands of colors in control. Because you need a different working strand for each block of color in the piece, you could end up with many strands of yarn hanging off the back of your work pretty quickly.
Some people wind up small balls of each color of yarn to work from (or use plastic bobbins made for this purpose, or homemade cardboard bobbins).
Others suggest that for colors you don't need a lot of or when you're working with many colors at once, just leaving a long strand of each yarn hanging free is a better choice. Start with a yard or so of each color and simply run your fingers through the strands when they start getting tangled.
This is much easier for some people to manage than using bobbins, but it will likely result in more ends to weave in as you'll run out of yarn more quickly. It's a small price to pay to save a bit of your sanity.
Keeping Tension Even
Another potential problem is keeping your tension consistent as you switch colors. Having heavy bobbins hanging from your work can make this problem worse, too, since they can pull down on the stitch and make it look different from the other stitches.
Pay attention when you switch colors that you're not knitting too tightly or too loosely with the new color. Slight uneven tension will also be aided by blocking.
Knowing Where You Are
Most intarsia patterns use charts to show you where to place the different colors and how to make the picture you're trying to knit, so being comfortable with working from charts will go a long way toward ensuring your success.