Arriving by Plane

You're only option for flying to Durham is to land at Raleigh-Durham International Airport (RDU), and this is a fine option.  At least for the east coast states, most airlines fly direct to RDU.  From the airport, a cab usually costs between $35 and $40 (that includes tip).  But unless you have a friend or family member to take you around, your probably better off renting a car, as there is no real metro system to speak of in Durham.

  Arriving by Train

Amtrak runs trains to Durham regularly from all over the country, not express though of course.  Some say a long train ride is the best way to see the country .

 Arriving by Bus

There is a Greyhound Bus station on Morgan Street in Durham, which runs right off of main street.  Like the train, there are very few buses, if any, that run express to Durham from anywhere in the country, but it is a cheap way to travel and see the south .

 Arriving by Car

According to MapQuest, it takes about 9 hours to get to Durham from New York, 13 from Chicago, and 37 hours from Los Angeles. 

Departing

Get out the same you got in.