When it comes to the CFA mile run...you really need to work on SPEED...going out and running "easy" for 20-30 minutes isn't going to cut it. Something like 2 sets of 8 x 200m (with a 100m jog in between each 200m and 400m jog in between each set) that is significantly faster than what you would average for 200m in a mile run (i.e. if you are shooting for a 6 min mile, that would be 45 secs for 200m...so 35-40 secs per 200m is about right). Adjust accordingly...you can mix it up (do 300m or 400m or a combination thereof on one day versus 200m or a ladder: 200m, 300m, 400m, 800m, 400m, 300m, 200m, etc.)...wouldn't recommend intervals below 200m or above 800m. When it comes to pace/times for your workouts, initially base it on what you can CURRENTLY run your fastest mile at right now. Then, as you get faster, update your times accordingly. One full lap around an outdoor track is 400m.
Edit: for clarification, you shouldn't be doing an interval workout EVERY day...you do need to have "easy" days in between to recover and rest days. However, the above are examples of the kinds of workouts you need to do.