Wellington sits at the junction of US-160 and US-81 in southern Kansas, about 30 miles south of Wichita. If you're coming from Wichita, take I-35 south to US-81 and head south — the drive takes about 35 minutes.
The nearest commercial airport is Wichita Dwight D. Eisenhower National Airport (ICT), served by most major domestic carriers. From there, it's a straightforward drive south. Wellington has no public transit or intercity bus service, so you'll need a car.