Common Mistakes: One - Buying tank and fish, together
This is the most common mistake done by the beginners, as well as some times by experienced hobbyists, too. Never put fishes immediately after setting up a new tank. Ideally, you should put the first fish in your tank, at least after week or two after the installation. You should fill the tank with water, add substrate, place the props like stones or drift woods, keep the air pump and filter running (also the heater, in case of winter season or chiller weather), switch on the light and maintain this 'fish-less tank' for a week or more. In hobbyists circle this phase is known as 'Fish-less tank keeping'. Few experienced aquarists also suggest to add little bit of fish food, regularly in the tank, even though there is no fish in the tank.
Though, apparently it looks ridiculous to keep an empty tank with filter, pump running and add fish food in that, but actually this is one the most critical phase of a new set up. This 'Fish-less tank keeping' ensures that the nitrogen cycle of the tank is running perfectly and you have built enough de-nitrifying bacteria in your tank to take care of the ammonia and nitrite to be produced from excreta of the inhabitants of the tank.
After running this fish-less tank for week (more if you have larger tank and have a plan to keep the little crowded), add fishes slowly. Never put a large number of fishes together in a new tank. This might cause a sudden ammonia spike and could be proved fatal for the livestock. I usually add, one or two very hardy fishes like, Sail fin mollies' and juvenile 'Common Plecos' (nice housekeepers for a planted set up) and wait for few more days before adding the central attractions of the tanks.
The image shows lily floaters in my planted set up.