Waskom is not located to a major airport, however it does offer a couple regional airports within a safe driving distance. The closest major airport is across the Louisiana border in Shreveport.
If you are interested in coming to Shreveport, you will most likely fly into the small Shreveport Regional Airport (SHV).
This is definitely a small town airport, and you will pay a higher price to fly into Shreveport as compared to New Orleans, or DFW... but it would save you a couple hours drive.
Waskom is not located near any public transportation, so unless you are on a tour bus on your way to Shreveport, you likely will not be able to get here in any other fashion. There are rental car facilities at the major airports around Waskom.