What is the best way to grow back hair in previously bald spots?

Depends on cause. There are many reasons for hair loss and bald spots, including heredity, telogen effluvium, alopecia areata, tinea capitis (fungal infection), and hair treatments. Sometimes hair loss may actually be an early sign of a disease, so it's important to see a dermatologist for evaluation. Depending on the cause, treatment can include topical corticosteroid and shots, rogaine, (minoxidil) and finesteride.