The first thing I'm going to tell you... DON'T ADD FISH YET!
So many people end up killing off perfectly good fish when they get their new aquarium. If you don't have patience, this may not be the hobby for you.
Once you get your tank set-up, and the water added, it's time to begin the 'cycle'. Cycling your tank is a necessary step to creating the best possible water conditions for your fish. It's the process that creates a natural, biological filter that helps keep the water clean and clear of ammonia (from fish waste) and nitrite, which are lethal to fish.
In a nutshell, when a fish does it's business in the water, it creates ammonia. One your tank is 'cycled', you have enough good bacteria built up in your system to remove it. So, the good bacteria gobbles up the ammonia and turns it into nitrite. The biological filter then converts nitrite and into nitrate, which is harmless... well, to an extent. We'll get into that shortly.
To cycle your tank, there are a few different methods: adding one or two hardy fish that you plan on keeping long term, using pure ammonia, or using fish food. (there's also a 4th method that I'll explain at the end).
I prefer the second or third. The goals for all 3 are exactly the same, but the second options are the most humane because cycling a tank can be very stressful for fish.
The the third option is the one I've gone with countless times (before I started using option 4, which I'll explain at the end). I grab a mesh media bag from the pet store and drop a raw shrimp inside. Then I hang the bag in the water and let the fun begin. (I've also just dropped pinches of flake food into the water as well, it works the same way). Basically, you want something to decompose in your tank so it generates ammonia. Once the ammonia starts to build, your colony of natural bacteria will begin to populate.
After a couple of days, I start testing for ammonia and continuing feeding the tank. Your ammonia levels will eventually spike off the charts, that's the first step. Keep monitoring the levels daily. Eventually, you'll see the ammonia level drop to zero. When that happens, you'll see a big spike in your nitrites, that's good. The third phase is the drop in nitrites and the spike of nitrate. Once you get to that point, start doing some small (10%) water changes to get the nitrates down. At this point, you should see 0 ammonia and 0 nitrite. You may see 10-20 in nitrate, but that's easily controlled through water changes moving forward.
Now, your biological filter has been created and you can add your fish without them dying after 24 hours. Patience is the key because the cycle can take several weeks to complete.
Keep in mind, if you're doing a reef tank, for example, invertebrates (snails, crabs, corals, etc) won't tolerate high nitrate levels, so keep the water changes going. I typically do 10% changes every weekend. Some people do 20% twice per month, and that's fine, too. Everyone's aquariums behave a little different so do what works for you.
Ok... option 4: now that I have an established tank in my house, anytime I want to set up a new tank, I can 'seed' it with sand, rocks, or filter pads from my existing tank to 'instantly cycle' the water. The idea being, the good bacteria lives in sand and on rocks, so if I take something that's full of the bacteria I need, and put it in my new tank, I won't have to wait for a colony to grow from scratch. If you've got a buddy with a tank, ask him/her if you can have a filter pad, sponge from a pump, rocks, or sand and add them to your tank. I use a mesh media bag for this and hang it in the tank so the bacteria can move in.
If you have any questions, don't hesitate to ask.