How would your average gym member who lifts incorporate sprints into his/her workout without getting too cerebral abouttt it?
Just do it!
Seriously, I would probably look at putting in a day or two of sprints per week before your weight training. Depending on your goals, the exact program could vary but if you haven’t done much sprinting before, start off easy and gradually build up your volume.
What are you trying to accomplish by sprinting? Getting stronger, getting faster, or using it to help you aesthetically? If its mainly the latter this may help:
building up speed endurance, dropping fat, and making the person faster.