While 1096 is the foundation date that Oxford chooses to assert for itself, we have little to no evidence to back up the idea that there actually was much, if any, teaching in the town at that early date.
To have any idea of what went on at the university (which before 1100 can have been nothing more a small community of church scholars dedicated to training up fresh generations of clerics – not a formal teaching institution in a sense we might recognise today), we need to move on to the period post-1167, the date at which the English king Henry II placed a ban on his subjects attending the University of Paris, which was at that time the pre-eminent educational establishment in northern Europe. In fact, as Brockliss points out in his recent history of the university, "the existence of Oxford as a legal and collective entity cannot be identified before 1214."
When an actual university finally emerges from these shadows, it is one that follows closely on the model already established at Paris and, probably, also at Bologna: "a self-governing ecclesiastical corporation of masters and students," which was recognised as such by the local municipal and ecclesiastical authorities, and which "explored the same texts with the same exegetical method" as its equivalents elsewhere in Europe.
Brockliss paints a picture of an institution that owed its emergence in part to its own early successes, which created masters "puffed up with their celebrity as intellectual superstars," and took inspiration from the then-emerging guild system to create a form of corporation that would offer these people the freedom not only to run their own affairs, but also to "boost their own power."
It was not until 1208 – a year in the university's history that we know something about, because it was the year of the murderous town-gown dispute that led a breakaway group of scholars to flee Oxford and establish a rival university at Cambridge in 1209 – that we can say a true university had begun to take shape. There is little reason to doubt, however, that this shape was based in large part on teaching conventions that had been established earlier than that, and may possibly, in some parts, have dated back to the late 11th century.
The first factor that set Oxford apart by this date was its separateness – all masters and students at the university, together with "various hangers-on, such as parchment-makers and scribes", received special privileges (fiscal and judicial) that distinguished them from the townspeople among whom they lived. This was a significant development, as previously such privileges had been extended only to churchmen who had actually been ordained, rather than to men who were still in training. The second was that it taught a curriculum – policed in parts by the Papacy, which had a clear interest in ensuring that theology, at least, was taught in a strictly orthodox manner – via several different faculties, those of the arts, theology, medicine, and law. Of these, the arts faculty taught the seven recognised liberal arts, which were grammar, rhetoric, logic, arithmetic, geometry, astronomy and music) and the three philosophies (ethics, physics and metaphysics). The law faculty was formally divided into two, since it taught both civil and canon (church) law.
So, Oxford can be thought of as having five founding faculties – but these were not equal. The arts faculty offered what we would now consider an "undergraduate" education, while the other four taught only "graduates". Arts, Brockliss says, were "considered propadeutic" – that is, their teaching provided the preliminary instruction required to allow students to move onto the "higher faculties" of theology, medicine, and law, and the Faculty of Arts awarded a preliminary degree, the baccalaureate. The theology faculty, the medical faculty and the two law faculties awarded master's and doctor's degrees, and these were required to admit students to the community of people capable of teaching others.
From about the same time, Oxford (and also Cambridge) developed a collegiate system which emerged from the establishment of hostels to house poorer students who could not afford to take lodgings of their own. The earliest at Oxford was University College, which dates its foundation to 1249 and was set up by its founder, William of Durham, to house 10 or 12 baccalaureate-wielding would-be masters of divinity. Balliol (c.1263) and Merton (c.1274) followed shortly thereafter. Cambridge claims that teaching began in the town in 1209, but its first college, Peterhouse, dates only to 1284.
Earlier responses here at AH can help to flesh out this basic portrait, and you may be interested in checking some of these out. I would suggest:
Oxford University was established c. 1096. How have applications and admission processes changed throughout these past 900+ years?, led by u/sungainstgold
I'm a student at the University of Oxford in the 13th century. How was a typical class taught?, led by u/Whoosier
and
How were students evaluated in Medieval universities? Did they give oral or written exams? How long did they last? led by me, u/mikedash
Source
LWB Brockliss, The University of Oxford: a History (2016)
Sadly the answer is it wouldn't have looked like much of anything...whenever universities are traditionally said to have been founded in the 11th century, and even in the 12th century, the date is almost mythological, or at least a very generous interpretation of "university". The traditional date for Oxford is 1096, and the date for Bologna is 1088, but there were certainly no universities there in the modern sense, with separate buildings in a separate area away from the rest of the town.
Education at that time mostly took place in schools run by the cathedrals or monasteries. Oxford didn't have a cathedral (it wasn't a diocese until the 16th century), but there might have been smaller schools in its churches or in the nearby monasteries. It wasn't really a centre of trade or law or religion or administration, so it probably wouldn't have attracted many students. A castle was built there in the 1070s, so that helped - and later, Henry II particularly enjoyed spending time there, and kings Richard I and John were born there, but that's many decades after 1096.
"The first master known to have been based in the town was the itinerant Frenchman Theobald of Étampes, who apparently taught the liberal arts or philosophy from about 1095 to the early 1120s.” (Brockliss, pg. 11)
But why was he there? Was he attached to any ecclesiastical or monastic school, or did it have something to do with the castle? Unfortunately we don't know. Oxford is a weird place to be in 1096, unlike London, or any of the dioceses or archdioceses with cathedral schools that would have been a more logical place to teach.
Theobald would have had to teach in a pre-existing house. Maybe he rented a room from someone and a few students came to listen to him. There were no separate buildings until the 13th century, well over 100 years after Theobald was there. In 1209, a student murdered someone from the town, there was a riot, and the students left the town for 5 years. The real origins of the university, in the sense of a separate corporation with its own distinct buildings, can be traced more to the return of the students in 1214. But even then, the first halls and colleges probably weren't built until the 1220s or 1230s (and the order in which they were built still isn't totally clear).
So if you were a student in Oxford in 1096, you might be studying in a school run by a church or monastery, and sometimes you might go to a rented room in someone's house to listen to lectures by a more famous visiting teacher like Theobald. But there was nowhere you could point to and say "this is the University of Oxford" - it simply didn't exist that way until the 13th century.
There are lots of histories of Oxford (including a giant 8-volume history!), but a more recent and accessible source is:
L. W. B. Brockliss, The University of Oxford: A History (Oxford University Press, 2016).