Greetings. Dragon gobies -- if by this you mean Gobioides spp., the big, grey-purple things with giant heads and tiny eyes -- are indeed brackish water fish. But they aren't difficult to keep. Nor is a brackish water tank difficult to look after. Apart from dissolving in a small amount of marine salt mix into each bucket of new water, everything else is the same as a freshwater tank.
So here's the deal with your goby. You can comfortably expect him to reach about 30 cm long, potentially quite a bit more, but that depends on the species you have (there are at least two species traded, one quite a bit bigger than the other). Wild fish feed primarily on two things: algae and tiny invertebrates. They hardly ever eat small fish, despite their reputation, and will only eat small fish if half starved. Under proper conditions, they are perfectly safe with livebearers of all types and few if any fry will be eaten.
Dragon gobies feed in three different ways. Firstly, they scrape algae from rocks. That's what their teeth are for. In the aquarium, algae wafers (sold for plecs and other catfish) are an ideal substitute. Secondly, they gulp plankton from the water. Live brine shrimp are the favourite for this. Watching them feed in this way is a lot of fun, and makes a good party trick for when people are wondering why you have such a bizarre looking pet. Finally, they sift the mud for worms and other small animals. Frozen bloodworms are a good substitute for this. Since you have three different ways to feed a dragon goby, you can mix it up over the week so that your goby gets a nice balanced diet.
The aquarium doesn't need to be complicated. Smooth, hollow ornaments (rather than lava rock) make the idea caves. Some people use long PVC tubes from hardware stores. Dragon gobies seem to love these. The rest of the tank should be sand of some type, ideally (smooth) silica sand or river sand. You could use coral sand if you wanted. Avoid gravel, because they can't burrow or feed properly in tanks with gravel. Don't worry about the sand becoming dirty -- the goby will keep it constantly turned over, and every time you do a water change, just stir the sand with a stick and siphon out any dirt.
Water chemistry isn't terribly important. The pH should be between 7 and 8, the hardness at least "moderately hard", and the salinity ~20-50% seawater (that's a specific gravity of 1.003 to 1.012). I'd aim for 25% salinity (SG 1.005) simply because that's easy to adjust your existing biological filter to without having to cycle it again. SG 1.005 is about 9 grammes of marine salt mix per litre of water.
Dragon gobies have no preferences for lighting, though you might choose to use quite bright lighting to encourage the growth of green algae on a selection of smooth rocks dotted about the tank. The dragon goby will happily snack on the algae. You could attach some Java ferns and Anubias to smooth rocks to create some shady spots if you wanted. These are tolerant of salty water and, being epiphytes rather than rooted plants, won't be disturbed by the goby.
As far as heating goes, the only thing to make sure of is the goby can't burn himself on the heater. Ideally, use a heater with a plastic cage around it. Some heaters come with these already. They're also available as accessories and don't cost much.
I hope that covers everything.
Cheers, Neale
Thank you so much. I am figuring out where to get some of those plants right now... Hopefully I will be able to set this up this weekend. Maybe I'll do a "journal" like I've been other people do here. And just for clarification the "dragon fish" I was talking about is indeed Gobioides broussonnetii. Thanks again!!
Now I want a dragon gobby! 
