My reenlistment date is approaching and I have been hearing about the Army Reserve Drill Sergeant. What does that entail?

Talk to the Reserve Component Career Counselor at the Transition point to see where the closest Drill SGT units are from your Home of Record. I know AD is giving 10K for an extra year that's hard to pass up. However prior AD will most likely get you a bonus for Reserve component Assignment as well but for 3 (5K) to 6 (10K) years.
Have your stuff together with PT, customs & courtesies, and D& C. Get back to basics in your head, being you're a SPC the basics should be pretty fresh in your mind. DSS (academy) was no cake walk when I went through but who knows now with things rapidly changing in the Army in terms of discipline and standards. Being a DS was the best time of my career and would go back in a heartbeat.

Talk to a BCT unit in your area. I know from experience they used to send SPC(P) to drill sgt school. The 108th controls all Drill SGT units and used to be based in South Carolina, but there are several commands under the 108th. Here in Kentucky the 95th I believe has the drill sgts.

Best option is to talk with a reserve drill concerning training, etc!