What a first medical involves
Student pilots exercising solo privileges need at least a Third Class medical certificate. The exam is the same protocol every pilot goes through: vision, hearing, vitals, urinalysis, and a general physical against the FAA standards, preceded by a review of the health history you file online.
A Third Class certificate issued before your 40th birthday is valid for 60 months. For most student pilots, one exam covers training and the first years of flying afterward.
If something in your history is complicated
Some conditions and medications require the FAA to review the application rather than the examiner issuing on the spot. That is not a denial, and it is not unusual.
Dr. Edmondson handles complex histories and special issuance cases regularly and will tell you exactly what the FAA needs. See special issuance and complex cases.