I've been told that the shiny side should go on the inside for cooking, and the outside for freezing. In other words, do you want to reflect the heat into the food, or away from the food?
However, common sense (which fails very often) tells me that with the temperature ranges involved, any benefit is marginal, if it exists at all.
The only time it might matter, is if you were trying to warm something up in the sun. Then it might make a difference.
EDIT: From The Straight Dope:
The truth is that the shiny side is
not treated with a dangerous chemical.
Mineral oil is used as a lubricant
during the rolling process, some trace
of which may remain on the finished
foil--but it's not dangerous. The
shiny side is shiny because of the way
foil is made. During the last pass
through the rolling mill, a double
thickness of foil is run between the
rollers. The side of each sheet that
comes in contact with the polished
steel rollers comes out shiny. The
other side has a matte finish.
http://www.straightdope.com/columns/read/1135/should-a-baking-potato-be-wrapped-in-foil-shiny-side-in-or-shiny-side-out
ALSO
The official word from the Reynolds
aluminum people is as follows: "It
makes little difference which side of
the Reynolds Wrap aluminum foil you
use--both sides do the same fine job
of cooking, freezing, and storing
food. There is a slight difference in
the reflectivity of the two sides, but
it is so slight that laboratory
instruments are required to measure
it."
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.
Best Answer
See this wikipedia page, it states that if not crumpled aluminum foils is generally safe, so make sure you do not crumple it. Then it says
The reference states
It also states
General Rules for Safe Use of Aluminum Foil:
My bolding.
So make sure you only cover the top of the cup and make the foil smooth, do not crumple it and it should be safe.
The reason to use this as stated in the blog is speed, a few minutes compared to much longer.