Oxford for students is a very small town; for most students, everything they need to get to (accomodation, lectures, tutorials, supermarkets, clubs etc.) is within roughly 15 minutes' walk. Of course, this has the effect that what would be an insignificant walk for students at most universities becomes an intrepid trek for Oxford students. But be aware that if you can walk comfortably any other form of transport is never necessary, but may be convenient.
Since Oxford is almost entirely flat (the few exceptions being St. Aldate's hill and Headington Hill) many students cycle. The prevalence of the Green Party has led to copious bike racks and cycle lanes so in general it's a safe place to cycle - although High Street is not for the faint hearted!!
Several of the large bike stores on the Cowley Road hold sales with "Freshers' Deals" at the start of each academic year one of which is hosted by the Oxford Union. In reality most freshers live close enough to the centre of town to never need a bike (unless they row) so these deals are more likely capitalised on by the 2nd and 3rd years. If you have an old embarrassingly-garish bike, it's probably a much better idea to bring that, as it's less likely to get nicked. A big D-lock is a good investment!
For girls in heels or students too drunk to cycle Oxford does have an incredibly comprehensive bus service, although it's also very expensive. The general services around Oxfordshire (such as the bus to Wallingford and Nuneham Courtenay) are actually quite economic (around £2.40 for a return to Nuneham Courtenay - 6 miles from the centre). Comparatively a return from St. Hugh's (around 1 mile from the centre) is £2 and to the Bingo Hall in Cowley (1.5 miles) is a similar price. Buses run to Abingdon, Blackbird Leys (read: the other side of Cowley), Jericho and beyond!
Very few students bring cars to Oxford with them, as the requirement that we live within 6 miles of Carfax makes everything within bikeable distance, and few colleges provide parking. Students living out may be lucky enough to have one space per house but further than that is unlikely. Driving within Oxford presents its own difficulties, with a confusing one-way system and mediaeval town planning that irritatingly didn't take cars into account.
Links with London
The Oxford Tube to London runs several times an hour, as does the Oxford Express. Journey times vary upon the traffic (and hence time of day) but while Oxford - London Victoria can be managed in an hour, it's safest to assume the journey takes 1.5-2 hours if you need to be there on time. Look out for discounted ticket vouchers at Freshers Fair.
Trains leave from Oxford station to arrive in Paddington, a journey that takes 1 hour (weekend stopping trains can take substantially longer). The station is around a 10 minute walk from the centre.