So, in order to use a private pilot's license, you need to have a valid FAA Class 3 medical certificate.
This is a very basic medical exam to make sure you don't have any heart problems, aren't on any medications that could interfere with your thinking or disable you, and can hear and see adequately. The hearing test is basically to make sure you can hear someone speaking softly on the other side of the room and the eye test is basically 20/40 near and far vision - with contacts or eyeglasses if needed.
Use of insulin to treat diabetes requires a "special issuance" medical certificate (basically an exception process) from FAA Medical headquarters.
You have to show that your diabetes is well controlled. You cannot have had any hypoglycemic incidence requiring assistance from someone else in the past year - and definitely cannot have passed out. That is what they are most concerned about with insulin - that you could pass out at the controls. You have to have a letter from your treating physician that documents this. You have to have had a dilated eye exam and have no active eye disease or eye complications fromn the diabetes. You have to have a cardiac stress test (ECG while on a treadmill) and the interpretation and original tracings have to go to the FAA Aeromedical office. This is to make sure you dont have any heart disease.
The whole package has to be sent to the FAA for approval. If they are satisfied, you will get a letter than lets you go to a local FAA Aviation Medical Examiner for the standard physical. If you pass that you get a medical certificate good for 1 year. To renew it , you have to go to your endo or other treating physician every quarter throughout the year and then and the end of the year he/she has to write another letter to the FAA stating that you remain in good control, have not had a hypoglycemic episode needing assistance, etc.
You have to test your BG before takeoff, every hour in flight, and 20 minutes before landing. It has to be in the range 100-300 mg/dl. If below 100, you have to eat a snack of 20 grams of glucose. If over 300, you must land at the nearest airport and not resume flight until it is within the range 100-300.
Note that these ranges are not particularly tight. They are more interested in your not passing out than your long term health.
There is a good book about an RAF fighter pilot who was diagnosed with type 1 diabetes while in the service and kicked out. He thought he would never fly again. Then he found out about the US license program for diabetics, got certified, and flew around the world. Here is his web site :
THe book is called Dare to Dream: Flying Solo with Diabetes.
Unfortunately, commercial flying is not allowed in the US for diabetics on insulin. There are some T1 commercial airline pilots in Canada, but I believe they have to have a non-diabetic pilot with them.