Making a claim to the EXP you've rightfully earned is the only way to get it. All students seeking to gain the EXP they've earned must post the accomplishment (conversation, enemy felled, etc.) that earned them the EXP. Only posts 'In school' or 'Out of school' count toward EXP.

Then a mod/admin must approve the claim, they'll add it to the student's total as soon as it's approved.