To set up a fresh water aquarium, you're going to need your tank, your strong stand. Remember water is very heavy, so you want to go with a designated aquarium stand. You don't want to just put a fish tank on a piece of furniture. I've heard nightmare stories, where the stand just collapses three months down the road, so you want to make sure the stand is very, very strong. For the filtration system, there are a lot of options. You can have a canister filter which goes in the cabinet, I prefer a canister filter for a freshwater aquarium because it is silent, the hoses run off the back of the aquarium, you can pack whatever you want inside the canister filter.
If you have the luxury of going with a wet-dry filter, like some people that had a salt water aquarium and now their modifying it to keep freshwater, you wont have any oxygen or very limited pH problems with a wet-dry filter because the water is being oxygenated constantly. It's a little bit more of an investment, the tank is going to be a little bit more expensive to allow for this type of filtration but it's basically salt water filtration applied to fresh water.
For most fresh water aquariums, you want to use canister filter, or a simple hang on the back filter, like the old whisper filters, the magnum filters, it just sits on the back of the aquarium and oxygenates the water, filters the water. You're going to want an air pump, because, fish are going to need a lot of oxygen and relying on the filter alone, usually isn't enough. So you'd want a strong air pump, put a check valve in the line, so the water doesn't back-siphon into the hose and flood the floor.
You're going to want a good heater, preferably a fully submersible heater, put it down a little bit low into the aquarium so when you do water changes you don't have to worry about having the top half of the filter exposed to the air. The temperature difference on the heater will crack the heater, so you want to make sure your heater is submerged very, very, low in the aquarium. You also don't want to put your thermometer right next to it. You want to put it away from the heater, so your picking up the true temperature of the water, not just the heated water next to the heater.
As far as the other things you need to set up an aquarium, you're going to want a lot of decorations. The fish need to feel secure but you don't want to do too much to where it just traps a lot of the detritus and waste, so just a good balance of decorations. I like to slope the gravel from the front to the back at a slight angle, visually it makes the whole tank become in focus. If the gravel is flat, it just doesn't look as good. Also, stack the decorations from small to high, put your high plants in the back.
Finally, go with a nice background decoration. You can buy things that you can tape onto the back. I like to spray paint the tank. You can use regal black or a blue spray paint. Do it when the tank is empty, do it outside, and let it dry real well, and you will have a solid background that should last years. That's it, just have fun.