I'm a student at the University of Oxford in the 13th century. How was a typical class taught?

You can find answers to several of your questions under “Universities” in our FAQs.

As for student life, though there were no “frats,” there might as well have been for all the carousing students did. One noteworthy features about university students, at least in northern universities they were cleric in minor orders (i.e., not priests but in the lower ranks that could lead to priesthood). As such they enjoyed immunity from prosecution in civil courts and also could not be assaulted by laypeople without their assailant incurring excommunication. These immunities obviously afforded them some leeway in their carousing. Surviving court records from 13th-century Oxford, for example, are filled with student crimes, major (murder) and minor (assault, out after curfew, etc.). These student immunities, among other things, were why there was often friction between “town and gown,” where “gown” is the students. Another thing to keep in mind: students started university at about the time modern students start high school, which probably increased their level of rambunctiousness. Like students today, they were also away from home for the first time and enjoying their independence. And, yes, they did pursue the local girls; Cambridge University was founded when an Oxford student murdered his “girlfriend” and fled the town. Town officials arrested and hung his roommates, causing the whole university (very small at the time) to flee. Some of them went to Cambridge and set up another school.

The great medievalist Charles Homer Haskins wrote a lovely article on medieval student life. It’s well over a century old, but still illuminating: “The Life of Medieval Students as Illustrated by Their Letters”. Here are some excerpts from 13th-century letters, which really are more “model letters” one could use as a template and personalize than something actually sent:

Son to dad: B. to his venerable master [i.e., father] A., greeting. This is to inform you that I am studying at Oxford with the greatest diligence, but the matter of money stands greatly in the way of my promotion, as it is now two months since I spent the last of what you sent me. The city is expensive and makes many demands; I have to rent lodgings, buy necessaries, and provide for many other things which I cannot now specify. Wherefore I respectfully beg your paternity that by the promptings of divine pity you may assist me, so that I may be able to complete what I have well begun. For you must know that without Ceres and Bacchus Apollo grows cold

Dad to son: To his son G. residing at Orleans P. of Besançon sends greetings with paternal zeal. It is written, “He also that is slothful in his work is brother to him that is a great waster.” I have recently discovered that you live dissolutely and slothfully, preferring license to restraint and play to work and strumming a guitar while the others are at their studies; whence it happens that you have read but one volume of law while your more industrious companions have read several. Wherefore I have decided to exhort you herewith to repent utterly of your dissolute and careless ways, that you may no longer called a waster and your shame may be turned to good repute.

“I have learned—not from your master (i.e., professor), although he ought not to hide such things from me, but from a certain trustworthy source—that you do not study in your room or act in the schools as a good student should, but play and wander about, disobedient to your master and indulging in sport and in certain other dishonorable practices which I do not now care to explain by letter.”

You’ll find lots of sources in the FAQ link but you can also read Haskins’ classic The Rise of the Universities (from 1923) for free.