Alton Brown recommends steaming them right in a normal tall pot with a steamer insert (your typical expanding/contracting one many people have on hand), directly in their husks. Basically, you put a couple inches of water in, and then a steamer insert, and the tamales (in the husks) go on top of the steamer.
You can find his recipe/method here.
You can also watch the episode on YouTube, go to about 4:45 in to see the tamales in the pot.
If you don't have a steamer insert of any kind, I would imagine you could fashion something out of aluminum foil without much problem. The most important thing is that you keep the tamales out of the water. In a pinch, an upside-down colander would work if you have a pot that's large enough to hold it.
Another (very low-tech) option is this hack, that basically uses a disposable aluminum pan to create the steamer/upside-down colander part of the rig. This seems like a pretty easy, straightforward solution.
Edit: as Michael points out in the comments, this seems like it could be a huge mess. I would recommend getting a disposable pie pan that's just smaller than your pot, poking holes in that, and putting it upside down in the pot like a steamer insert - seems a lot safer and more efficient than a large rectangle on top of the pot!
A couple thoughts... I haven't tried this, but I've heard of people doing it.
The microwave works relatively well to steam things. You could try "steaming" the dumplings in the microwave with a bit of water at the bottom of the dish or better yet, cover with a wet paper towel. You'll probably need to do some experimenting unfortunately. Under "ideal" circumstances, I'd probably prefer proper steaming, but this might work in a pinch. I imagine re-heating them would work well, but if cooking them works to your liking... no sense cooking them twice.
If you have a rice cooker, you could easily rig that up to "steam" as well. Just rig it up as if you were using a pot to steam it. Just make sure it isn't dry....
Best Answer
Maybe try using less water next time and boil the water before putting in the plates. Usually too much water is what causes the lower plates to have water.