The most important thing you can do is get more time out on the mountain. When I was first learning I used some of my vacation time to take Friday's off from work to get to a relatively nearby slope (2+hours drive).
Remember as much as you want to go straight, do not ride completely flat - it is a good way to catch an unexpected edge and get tossed. Try to find a relatively wide blue run that is not a zoo and practice making and linking your giant "S" turns. As you get nearer the bottom you'll find that you naturally elongate them to maintain speed.
Also be aware there are two types of riding/turning - cross over and cross under, you can find examples on youtube. Cross under is used a lot by park rats and by those who never really learned or like making big turns. It can also be situational, ie if it is crowded. You should learn both methods.