Air pumps are often advertised as low noise or "silent". It is important to be aware, that there will always be noise involved when running an air pump and depending on how sensitive you are, it will be noticeable.
But there are a few steps you can take to reduce noise. Most noise of air pumps is caused by vibrations between the pump housing and the environment. Additionally, the harder a pump has to work, the more noise it will make. Here are a few points that should help to quieten down your pump:
1.) If possible, try to position the pump above the tank or as high as possible. This will ensure that the pump has to work less hard to push out any air. In some instances this cannot be avoided, but there are additional steps we can take to reduce noise.
2.) To reduce vibrations, the air pump can be positioned on a thick towel or cloth. Foam works great as well (for example, Superfish are doing an "air pad").
3.) Some air pumps are coming with a hook, free hanging pumps will cause fewer vibrations (just make sure no hard housing parts are in contact with surfaces or are cushioned accordingly.
4.) Any type of restriction will increase noise level and decrease pump performance. Keep air lines as short as possible, avoid kinks and knots, keep valves and air junctions to a minimum.
5.) Air stones will get dirty and clogged over time, this will reduce pump performance and increase noise substantially. It is a good idea to replace those after a while or when simple cleaning is not enough any more.
6.) Air sponge filters will clog up over time, regular cleaning and wringing out of the sponges in dechlorinated water is important. Most of these filters can be taken apart for easy cleaning (the arms and outlet pipes usually pull off).
7.) Diaphragms will wear over time (this is not covered by warranty). This will decrease pump performance over time. Some manufacturers offer replacement parts to be purchased.