I took the DAT recently and did well on the PAT. I believe that practice is the best way. The Barons Book gives the best techniques to use to tackle each type. I followed the exact way they told me to do the problems and soon i was able to do them without always drawing them out. I got to a point where the only ones i missed were the Angle ranking. All i can say is practice practice practice. Time is also a big issue, the way i broke down the problems was like this:
1st section 10 mins
2nd - 10 mins
3rd - 5mins
4th - 7 mins
5th - 7 mins
6th - 10 mins
Review the last 11 mins. You will defineley need more time when you start but with practice the above time outline is definetley doable. Best of LUCK