Your first question is whether you are willing to make a student a full member of the board, i.e. one who has a right to vote.  If not, you can accommodate the student’s participation by merely inviting the student to the board meetings as a guest, perhaps with the right to speak (whether or not spoken to).  That wouldn’t require any bylaw change.  (You may want to obtain some sort of confidentiality agreement to protect against disclosure of truly confidential discussions of the board, particularly if the student will be required to report on the experience to a class at the university?)

If you want to make the student a full director with the right to vote, with actual fiduciary duties to the organization and subject to the same responsibilities as everyone else on the board, you would be dealing with your state nonprofit corporation law (assuming that you are not some sort of governmental entity operating under different statutory authority).  Most states require directors to be at least 18 years of age, so you would need to check state law and the student’s age to assure eligibility.  You could easily amend the bylaws to say that, in addition to electing the at-large directors, the directors would annually select a student director (or more than one if you want an expanded program) for a 1-year term.  If you elected a junior at the university, you could re-elect the person for the senior year if you wanted to, but, especially if board service was tied to a specific class, you would not be obligated to do so.  If you want to elect more than one student director but don’t want their votes to dilute the power of the board, again if permitted by state law, you could allow them to share a single vote, i.e. each of three student directors would have a 1/3 vote in matters of the board.  (If you allow only partial votes, you may want to check your quorum requirement to assure that you are not skewing it to give undue weight to the students.)

In general, you have a lot of options and opportunity.  It will probably work better if you create a separate class of “student directors” with a limited term and perhaps other limitations on their rights.