From the NE, including Chattanooga:
Take U.S. 72 west from Chattanooga. Entering Huntsville, U.S. 72 splits into I-565, use Exit 15 at Sparkman Drive and turn right. Turn right onto Lakeside Drive, then approach the roundabout, go left on John Wright Drive, turn right into Shelby Center Parking Lot.
From the South, including Birmingham:
Take I-65 North. Take exit 340 east to Huntsville. Use exit 15 at the U.S. Space and Rocket Center; turn left at the second traffic signal onto Sparkman Drive. Turn right onto Lakeside Drive, then approach the roundabout, go left on John Wright Drive, turn right into Shelby Center Parking Lot.
From the East, including Atlanta:
Take I-20 west to Birmingham, then I-65 north. Use directions above.
From the North, including Nashville:
Take I-65 South. Use Exit 340 and take I-565 east to Huntsville. Follow directions above.
From the West, including Memphis:
Take U.S. 72 east. Entering Huntsville, U.S. 72 becomes University Drive. After crossing the Sparkman Drive overpass, turn right at the next traffic light onto the UAH Campus (Putman Drive which turns into Ben Graves Drive on campus). Stay on Ben Graves Drive and follow the signs to the Shelby Center.
A UAHuntsville campus map is available here.