Start out with a glass tank or jar - just about anything will do, as long as it has a watertight lid. The ones we used were basically 6 inches x 6 inches, and 8 inches tall. But I think a container of just about any size will work. It's much easier, though, if you get something with an opening large enough to stick your hand inside (otherwise you'll have to arrange the plants using chopsticks). Also, Mary stressed that it was important to use a glass container - not plastic. Apparently, fairies don't like plastic! (And I don't blame them).
Inside the jar, you'll be making several layers to complete your garden. The first layer is a 1-inch layer of small pebbles (approximately 1/8-to 1/4-inch in diameter). After the pebbles, put a thin (1/2 inch or so) layer of activated charcoal (which you should be able to buy at the garden center or hardware store). Next comes a very thin layer of potting soil (when adding soil, less is more - since it's easier to add more, if you find you don't have enough, than it is to remove excess if you've added too much). I started with about 1/2 an inch of potting soil, and then added a bit more as I was positioning the plants.
Next, start planting some of the plants. We used Corsican Mint as our ground cover (although Baby Tears is another good choice). Plant this stuff sparingly, as it will spread - so make sure to give it room to grow. This is also the time to add other landscape features - larger rocks to form mountains, or special stones, or pebbles to create a footpath or similar. (Connor's has a cairn with a cave, as well as several stones meant to be chairs for the fairies). Fill in with extra soil if necessary, leaving a hole near the center of the garden to plant the "centerpiece" plant - try and make the hole exactly the right depth and width for the plant you intend to put there, so you can just set it right in the hole without having to add additional soil. For the centerpiece, we used Mother Fern, but I'm sure there are lots of other options, depending on how large of a tank you are using. (That holds true in general - there are loads of great plants, depending on how big and fancy you want to get - this site seems to have some excellent information).
It's important to remember that if you choose to include decorative items in addition to plants and stones, to use only natural things - and no metal, except for silver. (Fairies like silver, but dislike other metals - iron in particular is harmful, and will burn them if they come in contact with it).
Once the planting is complete, use a spray bottle (filled with water) to spray any dirt off the inside walls of the glass, and then water your garden until the water comes just to the top of the pebble layer at the bottom. Then, seal the lid on tightly, and place your garden in a sunny spot near a window (it must be near the window so the fairies outside will be able to see it, and know it's there; Connor went a step further and made a sign which he put up in the window, alerting all our neighborhood fairies to the presence of their cool new home). Don't be alarmed if the insides fog up at first - this is normal. If you want to remove the condensation, just take off the lid until the water evaporates from the sides. However, if you are in the habit of removing the lid like this, you'll have to water the garden more often. According to Mary, these gardens should only need to be watered twice a year, although you'll need to do it more often if you open the lid. In any case, when you can see that the water is almost gone from the bottom of the container, it's time to give it some more.
And that's it! Of course, you can do other nice things for the fairies if you like - Connor's been playing music from "The Nutcracker Suite" for ours, and they seem to enjoy it a lot.