The two closest airports to Clemson are the Greenville-Spartanburg International Airport (~45 min drive) and the Hartsfield-Jackson Atlanta International Airport (~2 hr 30 min drive). The most convenient way to travel to these airports is by car if possible.
There is an Amtrak station in Clemson that has daily trains to Greenville that depart at ~1:40am and daily trains back to Clemson from Greenville at ~5:30am. There are also daily trains to Atlanta that depart at ~6:00am and there daily trains back to Clemson from Atlanta that depart at ~11:30pm.
Make sure to check bus schedules as well for more flexible timings for Greenville travel. For Atlanta travel, note that the bus from Atlanta does not have an excellent track record (speaking from personal experience).