By plane
Chartered flights can be acquired to fly you in to Shawnee airport, most likely originating from Oklahoma City or Tulsa. There are no commercial flight charter services based in Shawnee, so arrangements for your eventual pickup would have to be made as well.
On foot
While towns in Oklahoma are quite spread out, some have been known to hitchhike especially along I-40. Not preferred.
By train
Originally established as a railroad hub, Shawnee still has many infrequently used rail tracks. While logistically difficult as well as illegal, it could be feasible to stow aboard a freight car inbound to Shawnee. Not recommended.
By car
Practically the only method of getting in or out of Shawnee is on the highway. Taxi cabs can be hired by calling a taxi service to have them pick you up, although doing so from another city could prove expensive.
There is an Enterprise rent a car in Shawnee and Shawnee Airport, so car rentals must be made before hand. Many times this is done at Will Rogers World Airport in Oklahoma City.
Most traffic enters and exits Shawnee via Interstate Highway I-40, although State Highway 3 and US Highway 177 pass through Shawnee as well.
By bus
Greyhound buses make daily stops in front of the American Colony motel on the far north side of Shawnee.
From there you will have to either call a taxi or arrange another form of pickup.