Oxford is close to London, with good transport links to most of the UK; it is easy to get to.
The closest proper airport is London Heathrow (LHR), which is a major airline hub. The easiest way from there to Oxford is to take the Airline bus, which runs up to every 20 minutes all day and night. Board at Stand 15 at Heathrow Central Bus Station (for Terminals 1 to 4), or Stand 10 at Terminal 5. You can stay on to the last stop at Gloucester Green Bus Station, from where you can walk or catch a taxi.
Alternatively, get off on the High Street at Bus stop J1, walk 100m further west along High St, and turn right up Catte St for a nice 30-minute walk towards the colleges. There are roadworks at St Clements, which means that incoming buses take a detour and miss out the stops between Gipsy Lane and Gloucester Green. You can buy bus tickets in advance or on the bus; but note that the bus driver takes cash (GBP, EUR, USD) only. The journey takes about 100 minutes from the Central Bus Station, 90 minutes from T5, assuming no traffic delays.
You can also take the Heathrow Express train to London Paddington (PAD) station (taking 15 minutes, every 15 minutes), and from there a train to Oxford Station (OXF) (taking an hour for an express train, about four per hour). This is usually quicker than the bus, but it’s more expensive, and Oxford rail station is less central than the bus station.
London boasts at least four other airports. London Gatwick (LGW) mostly provides short-haul and holiday routes; you can also take the Airline bus (Stands 1/2 at the South Terminal, Stands 4/5 at the North, taking 2+ hours, up to every hour, same stops in Oxford as the bus from LHR). London Stansted (STN) and London Luton (LLA) mostly provide flights on budget airlines; National Express Bus 737 takes a convoluted route from Stansted (four hours to Oxford) via Luton (two and a half hours to Oxford), but only three times a day. London City (LCY) is in East London; you can use the London Underground to join up with rail or bus routes from London to Oxford. (In fact, the former Kidlington Airport (OXF), five miles north of Oxford, was recently rebranded as London Oxford Airport, making at least six… but unless you have a private plane, you won’t be flying there.)
Other plausible routes are through Birmingham Airport (BHX); you can take the train from Birmingham International Station (BHI), which is directly connected to the airport, to Oxford Station (trains hourly, taking an hour, but the last one at about 10pm). Or through Southampton Airport (SOU), then take the train from the adjacent Southampton Airport Parkway (SOA) station to Oxford Station (trains twice an hour, taking about 75 minutes direct, but last one at about 10pm).
Oxford has two rail stations, Oxford Station (OXF) on the west side of the city, with connections to Reading, London Paddington, Birmingham New Street and northwards, and Oxford Parkway (OXP) to the north, with connections to London Marylebone and the Chilterns. Oxford Station is within walking distance of the city centre; but the Park & Ride Bus 500 from Oxford Parkway conveniently comes down Banbury Road close to all the college accommodation. Train timetables and route planning are available at National Rail; you can buy advance tickets online, and sometimes get cheaper fares to travel on a specific train.
There are cheaper and more frequent but slower buses from London to Oxford than the train, run by two competing companies: the Oxford Bus Company X90, and the Oxford Tube. Both run day and night, at frequencies from every 12 minutes to every hour, taking about two hours, but with slightly different boarding points in London.
Arrival by car is strongly discouraged: Oxford is a small ancient city, and what little parking there is is inconvenient and expensive. If you arrange your own accommodation in a hotel or B&B, they may be able to provide parking, but the colleges probably can not. You can in principle park in one of the five Park & Ride carparks around the ring road, and take a bus into town; but there is a penalty fee for parking longer than 72 hours. For short distances within the city, it is almost certainly quicker to walk than to drive; or to take a taxi in case of mobility constraints.
Not ridiculous, if you’re energetic. The UK has a National Cycle Network of mostly traffic-free routes. Oxford is on National Cycle Route 5 between Birmingham and Reading, NCR51 to Bletchley and Cambridge, and NCR57 (not yet complete) between the Chilterns and the Cotswolds.
There are taxi ranks at the railway stations and at Gloucester Green near the bus station. Elsewhere in the city, you can hail an empty “London” taxi if you see one, but they are rather thin on the ground. You can also phone or use a mobile app to book a minicab—these are licensed only for pre-booked passengers, so you can’t hail one on the street. Companies include ABC Radio Taxis on 01865 242424, 001 Taxis on 01865 240000, and Royal Cars on 01865 777333. All three companies also offer pre-booked airport transfers; these are significantly more expensive than the bus or train, but may be worthwhile if you can get together a group of people.