I am a cyclist, and former runner (ran a lot in the Marine Corps) always did the 3 mile at around 19 minutes flat.
That said, thats not blazing fast, but in hind sight, i have learned a few things that would have applied to running that have made a big improvement in my cycling.
First off, you need a fitness base. If you havent been running you are going to hurt all over for a little while. Generally I have found that a fitness routine doesnt start feeling like a routine till about a month in.
As far as workouts go, if you have extra weight you need to burn off, start running longer distances and compensate by lowering intensity. This is not going to make you much faster but will get your body in the condition to get faster.
If you are at a good weight, start off easy.. but the key to going faster is to go hard. After a couple of weeks figure out what you can do in a 20 minute maximal effort. Once you get an idea of what that kind of pace feels like, you will be structuring your speed workouts around that
Once a week work in a couple of intervals of 10 mins at the 20 minute pace with 10 minute running rest inbetween, another day do 5 minute intervals at a faster pace than your 20 minute time. You should feel like you are giving your all for the 5 mins. Figure out how many of these you can do with 5 mins of rest between them. 3 of them will give you a 30 minute total run time. I would mix in a third hard workout in the week of spontanous intensity, like trail running with a friend that is fast. Look at keeping it at 20 mins of max intensity.
Beyond that, rest rest rest. Other days you can fill with light runs for active recovery
Im no expert, but one thing I have definitely learned is that you won't get fast if you don't run fast. Just putting miles in will keep you at the kind of pace I was running (that was my mistake).
In the short while I was using a similar regimen to the one I posted above but for cycling, my power improved dramatically all the while having a smaller training volume.
