I do a very general workout three days a week, but have added a few specifically for doing tandems.
General Workout - I do three laps of the weight machine, 10 reps at each exercise. I've been doing it off and on for about 12 years now, and I really do feel better when I'm "on".
Tandem Specifics: 1) I do a lot of pulldowns. Three different kinds. One was modified to look and feel more like flaring. I got tired of the big guys "helping" me flare, and do all the landings myself now.
2) I do a pull that simulates tightening the laterals - I stand with my back to a pulley about elbow high, and pull outward. Again, I feel better doing it myself than having the student help.
3) I sit in front of the same pulley I do upright rows and curls with. With my legs straight out in front of me, I hook the bar over my toes, with my heels against a board (as a stop). Pull your toes toward your knees. That helps when you have students stand on your feet while you adjust the harness after opening.
When I started working out, I spent some time with a fitness coach to learn how to work the equipment, and get a balanced workout. I'd recommend that to anyone starting out. That would also be a good opportunity to tell them what hurts after a weekend of tandems, or what you'd like to be able to do better. Most can help you develop a workout to target those areas.
I use an amount of weight that is challenging but not painful. When it starts to get easy, I do a few more reps for a couple sessions, then increase the weight, and be prepared to back down on the number of reps per lap.