Gateshead can be accessed from the north on the Tyne and Wear Metro from Newcastle. The metro goes to the main bus and metro interchange in the town centre. Also from Newcastle there are regular buses, which often carry on to most parts of Gateshead. From all other directions, the bus is the best option.
You can get a train to the suburb of Heworth. Alternatively, there are stations in Dunston, MetroCentre and Blaydon.