The way I'd approach this problem may vary depending on what information is available about the aircraft and flight condition you are analyzing, but here is a rough outline of how I'd suggest approaching this problem.
- Determine aircraft CG location and wing center-of-pressure. Both of these things should be fairly straightforward to determine, or reasonable approximations can be made. With this information, you can determine the aerodynamic force required of the horizontal stabilizer to balance the pitching moment. You can start with some assumptions to make the calculation more straightforward (e.g. the horizontal stabilizer is the only element contributing to the pitching moment) and then relax them as needed to improve the result depending on which ones are valid for the flight condition you are considering (e.g. in a gliding flight condition there would be no thrust contribution to the pitching moment.)
- By balancing the moments you'll get a value for the lift produced by the horizontal stabilizer. To get drag, you'll want to determine the local angle-of-attack, as well as the elevator deflection required, which depends on the flight condition. If you have information about the horizontal tail airfoil, planform, and other geometry, that will be helpful too. You'll want the angle-of-incidence of the horizontal stabilizer and wing to determine the angle-of-attack at the horizontal stabilizer (again, start with restrictive assumptions about no downwash from the wing, and relax as needed.) You can consider the effect of a trim tab (if used) as well. This should start coming together to give you a value for drag.
Depending on why you are calculating these loads and how you are bookkeeping your aerodynamic forces, you can also consider interference effects.
In terms of resources, I learned a lot from Airplane Aerodynamics & Performance by Jan Roskam. If you get the book and continue reading the section below, it should reference other sections in the book to help you piece together all of the aerodynamic contributions you are interested in. There may be other better resources than this one, but this is simply what I am familiar with.