By plane
The city has a small airport of its own, Columbia Regional AirportCOU, which offers a limited number of daily flights to/from Memphis International Airport in Memphis, Tennessee.
MO-X (http://www.moexpress.com) pronounced 'moe-ex' operates an airport shuttle service that does door-to-door pick-up/drop-off from town to airport St. Louis and Kansas City airports & vice versa for about $44 each way, $82 round trip. It takes approximately two hours to reach St. Louis airport STL and a little longer for Kansas City airport MCI. It's rather slow, since it'll stop to pick up multiple passengers and so on.
By car
The city is accessible from Interstate 70, exit numbers from 121 east to 130. From the north and south, use U.S. Highway 63.
If you choose to drive, it'll take about 1 hour and 45 minutes to 2 hours from/to St. Louis Lambert International Airport STL112 miles, and about 2 hours and 15 minutes to 2 hours and 30 minutes to/from Kansas City International Airport MCI150 miles. Long-term parking is around $8/day at St. Louis airport and around $5 at Kansas City airport.
Megabus
(http://us.megabus.com). Low-cost carrier offers service once-daily service to Columbia from Chicago, St. Louis, and Kansas City. Fares start at $1 when ordered well in advance. Bues stop at the bus loading area behind Wabash Station, which is located at East Ash Street and North 10th Street.