Norwich's good train connection reflects its importance in Victorian times when there were three large train stations in the city. After the other two closed down, Norwich Thorpe became the main station. The station is located east to the city centre with most places of interest within walking distance.
Hourly services are available to Liverpool, Cambridge, London/Liverpool Street, Great Yarmouth and Sheringham. Many cities on the route like Ipswich and Peterborough are well connected as well. It can be reached from most places in East Anglia within less than 90 minutes, making Norwich a good day trip destination.
To get cheap fares, I recommend to use online booking sites like Thetrainline.co.uk . Please keep in mind that off-peak return tickets are cheaper than two single tickets or travelling in peak times.
Useful bus numbers
Bus number 25 goes from the station in to town and onto the University, use this bus for Unthank Arms and Mad Moose.
Bus 35 goes from the station to the university through town but not near the pubs
You can get around Norwich city centre on foot, there is no need for a car.
However, if you want to explore the best bits of the North Norfolk coast you will need a car.
There is a local train service to the coastal resorts of Cormer and Sheringham. Some of the smaller places are served by an infrequent bus service. I've noticed that the local bus company generally puts on the oldest most dilapidated buses on these routes!
You will see so much more with a car.
There are trains from Liverpool Street station in London. The trip take about 2 hours. The company that runs the trains is called One Railway. You can get cheap tickets if you book in advance. Check out the website for latest deals.
You can walk from the train station into town but if you have luggage you might want to get a taxi from the taxi rank outside the railway station.
Parking is next to impossible in Norwich - but all is not lost! The buses are frequent and inexpensive, for example, the No 25 from the railway station into the city runs every 10 minutes - that's if you can't be bothered to walk mostly uphill for about 20 minutes. If you must travel to Norwich by car, there a numerous park/ride car parks surrounding the city with frequent bus services into the centre.
You can get from London to Norwich by train from Liverpool Street Station. It is a 90 minute ride and costs £66 return peak (April 2007), there are cheaper rates I believe after 7 o'clock.