By visiting a doctor and filling out lots of paperwork. I wonder if you could cut down on some of that if you just grow a moustache?
A student who wishes to obtain a beard exception must visit a BYU Student Health Center doctor by appointment (422.5156). The doctor will fax his recommendation. The student then needs to come to the Honor Code Office to fill out some paperwork and receive the letter allowing the growth of the beard, if approved. If a yearly beard exception is granted, a new Student ID will be issued after the beard has been fully grown, and must be renewed every year by repeating the process.
If a request is granted for a temporary or more permanent beard exception the student will be notified by the Honor Code Office; at which time the student will come into the office to complete the necessary paperwork. After completion of this process the student may then grow a full beard according the guidelines given.