Can a person with Type 1 Diabetes get a medical and learn to fly?
As far as the FAA is concerned your friend can get a medical, but he will need a special issuance medical, will only qualify for a third-class medical, and will be prohibited from operating aircraft outside the United States.
In addition there are some specific requirements to obtain the special-issuance medical for insulin-dependent diabetics, and monitoring requirements before and during flight which must be adhered to.

The FAA has a page of guidance for Aviation Medical Examiners that deals with insulin-dependent diabetes which your friend should review (and be prepared to discuss with their AME).
Diabetes.org also has a page on Diabetes and FAA Certification, and AOPA's medical folks would be a useful resource to help ensure that the special issuance medical goes through without any hiccups.