Best Way to get there is most probably by Train:

By Train:

There's a train pretty much every 10 mins from Darlington to Durham and quite cheap at £6.20 return.

How to get to the ground: (Best and Cheapest)

After getting off at the train station, make your way to Durham bus station which is about a 5min walk. From Durham bust station the Sunderland bus (No. 220) leaves every 10 minutes. Get off at the B&Q stop and walk forward for approximately 50metres to the mini-roundabout. Turn left and continue to the traffic lights. Turn right at the lights and the football stadium is approximately 150 metres on the left.

Alternative way's to get to the ground:

If your a keen walker, the ground is about a 2.5 mile walk from the trainn station or you could get a taxi straight from the train station for about £8.

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You need a column in the home programme advising away day travel..great work big lad.

You need to be a very keen walker to walk from the train station as it's an uphill walk to durhams ground....with the odd boozer sort of on the way.

If you can get a taxi that's easiest. Although as Tim says the bus station is near the train station