My experience practicing for the APFT:
Push Ups: do some different types to help improve your arms' overall strength. When you practice the 2 min of push-ups, do NOT stop before the time is up; if you feel like your done, pause (in the position where your arms are not bent) for a couple seconds then keep going.
Sit-Ups: Same advice; bang them out, pause momentarily if you feel like you are done, then keep going. As my amazing marine gym teacher told me one day, you will do far more if you take two seconds to regroup then if you push out two more sit-ups when you are already dead and fall over before time is up.
The run: I feel your pain. This time last year the concept of running 2 miles scared the heck out of me. I can't say I've been running as much as I should, but the work I have put into it has made it so every time I've run 2mi in the past couple months I have passed. The key to this would be to develop a running routine. Pick a time of day to run (start at every other day, then you can add days if you wish) and stick to it. If you run at sporadic times it is easy to skip it one day, then another day. Routines keep you working hard, because they become habit. Do some other forms of cardio as well to improve your endurance, such as biking. Surprisingly, using a stationary bike at the gym actually improved my endurance a lot.
Good luck!