Once you're on a program, most likely with one of the many training groups in the Chicago area, you will begin seeing results as early as one month into your new training regimen. This will vary by the runner. Generally, it's within a month. Bud James, who coaches athletes in the south suburban area, agrees with the time frame necessary to get your race times to the next level. It takes the body that long physiologically to accept the training.
Most top runners can round into decent racing shape in six weeks.
Average folks will take more like eight to 12 if they consistent and to the correct combinations. That tempo work will get you ready for intervals. Then, the easiest way to get into it is to find some hills to run. It helps get you used to doing something at a faster pace, without causing any injuries. I'd say any kind of hill work is a great stepping stone to speed work.