The best advice I can give is that you're not going to want to use full power very often. I find that food tastes much better if you cook it for longer at 60 or 70% power then if you blast it quickly at 100%. This is especially true for proteins like chicken. I guess this allows for slightly slower, more even heating without destroying all the water in the food. The extra minute or two of time is worth the huge difference in the final texture.
I find that pretty much any vegetable or rice-based dish will reheat "ok" in the microwave, because of the nature of the microwave itself, which works very well for steaming. When reheating stuff like this, throw a tsp or Tbsp of water in the container, and place a lid on it (but do not seal the lid, you want it vented slightly). Again, stick with less than full-power.
I know someone who swears by boiling a glass of water in the microwave first to fill it with moist, warm air. Supposedly it helps with evenness and faster cooking, and reduces drying out the food; I don't know if I buy it but thought I'd mention it so you and the community can comment/decide. I understand the idea, but feel like you'd lose so much of that just opening the door to swap the water for your food. If you do go this route, it's very important that you understand superheating water, which is dangerous. Don't try to boil water in the microwave without reading that link.
If you're adventurous, there's a line of Corningware Microwave Browning products (scroll about halfway down the page where it mentions browning) - I was given one a half a year ago and was surprised at how well it works. There's a lining of microwave-safe metal (I believe tin oxide) inside the bottom of the casserole/skillet, and you heat the casserole by itself for a minute or two first which gets that blazing hot. When you drop food on it, it actually sizzles, so now you're using a combination of normal microwave cooking and direct, skillet-like heat. I've had a lot of good luck reheating things like pork chops and keeping/adding a crust to them.
Also, there's a book, Microwave Cooking For One, and an accompanying website, that are both supposed to be really useful. I don't own the book but have heard from friends who do own it that you can learn a lot about general microwave use from it - even if you don't plan on cooking from "scratch" and are just reheating leftovers.
All that said, I completely agree with Jefromi's comment. 90% of the food I reheat is reheated in the toaster oven, either preheated like a regular oven, or under the broiler depending on what the food is. You might take an extra 5 or even 15 minutes to reheat this way, but the difference is unbelievable, and the convenience is still the same - I just put whatever I want to reheat into a casserole dish and throw it in, sometimes covered, sometimes not. So, cleanup still only involves one dish, and you can eat directly out of it (though it will be very hot, so be careful!) Once you get into the habit of using the toaster oven, you'll find a way to make up for the small amount of extra time - for example I often I empty the drainboard while it preheats, and wash dishes or something similar while the food heats up.
For me, I use the microwave's power setting. This is sometimes a misunderstood feature. When you don't set the power level, then it is 100%. This means during 100% of the cook time the magnetron inside the microwave is active and radiating your food. If you set the power level to 10, then during the cook time, the magnetron will not be active the entire cook time, instead it will be active during 10% of the time. "Power" is a bad term because it does not effect the power level of the magnetron. It affects the amount of time it is active.
This is helpful to know if you also understand that microwave energy does not penetrate very deeply into your food. It enters about 1 to 2 inches. This mean the surface of your food gets really hot when the magnetron is on, but the deeper parts are not getting hot. You use this to your advantage by setting a lower power level which allows the heat to conduct through your food naturally when the magnetron is not active. It is a way to warm the entire product without blasting the outside of it.
If you are microwaving something thick, then reduce the power and increase the time.
If you have a microwave safe shelf, then use it! That allows more microwave energy to come in conduct with more of your food's surface. The waves "bounce" inside the box, so being on a shelf lets some wave bounce under it and hit the bottom of your food.
Best Answer
The CorningWare browner works on a simple principle. It is lined with a material that can absorb microwave radiation (just like water does) and therefore become hot. Then when you add your food, the hot surface of the pan browns it. Seems like an effective solution in the situation you describe, where you really want to cook with a hot surface but can't use normal means in the enviroment you are in.