Hi, Liza -
Your best bet is to drop your needle now and then so it hangs towards the floor and allows your thread to untwist itself. Most problems with tangling threads are due to the embroidery floss becoming too twisted as you work with it, so that it winds up as you pull your thread through, often resulting in a knot. If the knot forms on the back of the fabric, you don't always catch it until it's too late to take it out easily - you end up stitching through it and so forth, making it almost impossible to get it out. So I'd suggest dropping your needle and letting it hang towards the floor every now and then (say, every five stitches or so). An alternative to that would be to roll your needle between your finger and thumb every time you take a stitch. If you get in the habit of pulling your finger back on your thumb while holding the needle, this will keep the thread from twisting up on itself. And yet another alternative (but a lot harder to get used to) is keeping the needle in the same position as you pull through the fabric, making a conscientious effort not to turn your needle as you stitch. But this latter approach is rather difficult to master. The easiest approach would be dropping the needle now and then.
Ah - another thought, too... some threads are more prone to the twisting and tangling dilemma than others. If you're just using regular stranded embroidery floss, make sure you're using a good floss, rather than an off-brand "craft" floss. For example, DMC and Anchor are always good bets.
Hope that helps!