Welcome to Fishlore!
http://www.fishlore.com/aquariummaga...ngbeginner.htm
A little shameless plug here. This article contains way more information than I can write in a post (there are a total of five chapters, links at the bottom lead to the next chapter)
Other than that, here we go.
ThisGuy's right. One thing we need to know is aquarium size.
If you show your parents one thing, it should be this line:
For a first aquarium, bigger is easier.
There is a limit, of course, but 10 is better than 5, 20 is better than 10, and 40 is better than 20. The reason is that water chemistry is easier to maintain in a larger tank.
Some things you'll need:
A tank (duh

)
Filter (specifics on this will depend on aquarium size)
Heater (unless you've got a big tank with goldfish)
Substrate (gravel, sand, etc... This is determined by expense as well as the inhabitants of the aquarium)
Decoration (this could be anything from live plants, rocks, and driftwood to resin statuaries. Most fish need something to hide in/behind, however, so you should have something)
Clean bucket that has been used for
nothing. Buy a new one. If you have a 10g or bigger, get a 5g bucket from a hardware store, otherwise, you can get smaller ones at pet stores.
Water change equipment (usually a simple tube with a wider attachment for vacuuming gravel)
Net (needs to be appropriately sized for the fish)
Fish food (This will depend on the fish, too)
Water conditioner (we suggest Prime or Ultimate around here)
Water testing kit
One last thing, and this is covered in my article:
Please please please please please, for the sake of the fish, cycle the tank fishless.
My article covers it, as does this article
http://www.fishlore.com/NitrogenCycle.htm