Talk to Your Coach or Athletic Director
You should first discuss your need for a visor with your coach or athletic director. Why do you need a visor? To prevent eye injuries? To prevent damage to an existing eye injury? Sensitive eyes? Migraines due to a light sensitivity?
Your coach or athletic director should be able to tell you about the rules specific to your league. Certain states, New Jersey for example, allow only non-tinted visors. And your team might have its own policies about visors.
Talk to Your Team Doctor
Discuss your need for a visor with your team doctor. Although he might not be able to write you a prescription for the visor, he should be able to answer sports-specific questions about eye concerns. He also might be able to give you a referral to a specialized eye doctor who can write the prescription. Getting a referral from a sports-medicine specialist can help ensure that you get your prescription in a timely fashion.
If you decide to bypass your team doctor and seek out an eye doctor on your own, make sure you are clear and upfront about your needs when you book your appointment. Explain on the phone that you need a doctor who can write a prescription for a football visor and that you are seeking an appointment specifically for this purpose. If the receptionist isn't sure whether they have a doctor who could or would do that, request that she find out before you agree to an appointment.
Talking to the Eye Doctor
When you visit a specialist who can write a visor prescription, be honest about your needs. If you're simply afraid of an eye injury, say so. Don't make up pre-existing eye conditions, as the specialist would be able to debunk these claims and then would be less likely to write you a prescription.
Note that if you go to your eye appointment on referral from a sports medicine specialist, your eye doctor may be more willing to write the prescription for a visor without a lot of questions and tests because she will know that you have already discussed the matter with a physician.
Obtaining the Visor
A prescription for a football visor won't be "filled" like a normal prescription. You can't take it to your corner pharmacy and walk out with a visor in a little white bag.
In fact, football visors can be ordered online (see references) without a prescription. Your team's equipment manager would also be a good resource for ordering and obtaining a visor.
The prescription in this case is not an authorization to purchase, but a license to use. It is proof to coaches and league officials that you have a medical need to wear the visor during games, so be sure to keep it with your gear in case it ever comes into question. You might want to ask an assistant coach or manager if they can hold on to the prescription on the sidelines during games.