The best ways to travel around the UK by mass transport are train and bus.
Train - (http://www.nationalrail.co.uk/)
The train network is very extensive. Your best source of information (including fares and time -tables) for trains will either be the Internet (using the link given above) or the Cambridge train station. The train station is located on Station Road, off of Regent St. From City Centre, it is a 15-20 minute walk or a 5 minute bus ride (for just under £1). Tickets are to be purchased prior to travel at the station's ticket window and are then checked on the train by conductors. As a student, you are eligible for a Young Person's Railcard, which costs £20 and gives you 1/3 off most fares within the UK. You can purchase a Railcard at the Cambridge train station with a form of ID and a passport photo (they make it for you on the spot). Seeing as the card, which is valid for one year, will save you about £7 on one return trip to London, you will likely find that it
is a wise investment. (There is actually an entire website devoted to the card: http://www.youngpersons-railcard.co.uk/.) Typical options are same-day return (cheapest), and open return (most expensive).
Bus (http://www.nationalexpress.com/neh.cfm)
If there is a town that you can't get to by train, you will probably be able to get there by coach. You can also take a coach right to the center of London (Victoria Station). National Express is the major provider of coach services; you can find time tables and fares on their website or at their office near the bus station on Drummer Street. Consider buying a Student Coachcard (called an NX2 card), which will save you up to 30% on ticket purchases. If you're up for the longer bus rides (instead of trains), MegaBus can save you bundles on traveling within Great Britain (www.megabus.com), and
Cars
If you plan to do British sightseeing that takes you outside of the major cities (e.g. Stonehenge, Stratford upon Avon, Warwick Castle, or the British countryside), you may find that car is the most logical travel option. A map would be a wise choice, but you'll find that road signs are informative and plentiful (even away from cities).
Eurolines might be able to get you to places in Europe and back for cheaper than flights if you're up for the long rides (http://www.eurolines.com/).