Ok, so let me explain it!
Fish produce waste in the form of ammonia- basically "peeing" in the water. When leftover bits of food and fish poop break down they also produce ammonia. This is super toxic and will kill your fish! It's why goldfish seem to live such short lives- the ammonia builds up and kills them (The actual average lifespan of a goldfish is around 20 years!)
The remedy for this is that there are special bacteria that will convert ammonia into nitrite, which is also toxic, and then another kind of bacteria will convert nitrite into nitrate, which is only toxic in high amounts. Just change some of the water ever week and you'll remove the nitrate and have a healthy fish tank!
The trouble is that this bacteria takes some time to grow. You need to have the tank's filter set up and running and a source of ammonia for the bacteria to "eat" in order to grow this bacteria.
The two main ways of doing this are "fish-in", which is where you add a few hardy fish at a time and slowly allow the bacteria to grow. This method is very work-intensive; you need to do daily water changes of around 50% for the first month or so. The other way is called fishless cycling where you use a non-living source of ammonia, such as a bottle of ammonia from a dollar store sold for cleaning, or a cocktail shrimp in panthose hanging in the tank decomposing. This method is almost effortless, but it also means you'll have an empty fish tank for about a month and then you can add all of your fish at once.
Either way, the trouble is it takes about a month on average to cycle a tank and the only good way to speed up the process is to get filter media from an established tank. Hence the tricky part of setting up a tank overnight like that.
Here's guides to both kinds of cycling:
http://www.aquariumadvice.com/the-almost-complete-guide-and-faq-to-fishless-cycling/
http://www.aquariumadvice.com/forums/f12/fish-in-cycling-step-over-into-the-dark-side-176446.html
Some more questions: What kind of fish do you plan on getting? As a heads-up, goldfish actually get way too big for a 10 gallon. There are lots of beautiful tropical fish you can get though, and they're actually EASIER than goldfish to care for!
No matter what you do, make sure you have a heater, a good filter, and an API freshwater master test kit. Those are the 3 most important pieces of aquarium equipment.
I know this stuff can be overwhelming! But don't be discouraged- it's actually a lot easier than it might seem. Feel free to ask tons of questions!