There are a number of maintenance tasks that I perform regularly in order to keep a piano at its best, mechanically and sonically 

The regulation I am describing here is for upright pianos and although Grand piano regulation is in some ways similar, it necessitates the removal of the action from the piano in order to regulate and is therefore more time-consuming.

Piano keys sometimes need either easing, or the opposite; if the key is sticking, the felt bushing can be eased with pliers but also, lateral movement can be eliminated by manipulating the oval pin underneath the key at the front, resulting in the feeling that the keyboard has been "tightened up".

The most common task is the regulation of either the screw or the capstan that adjusts the amount of play between key and action. This ensures that the action assembly operates correctly in terms of the hammer blow and its set-off and check, both of which may also, as a result, need regulation.

Also common is the need to space the hammers so that they strike the strings centrally, although if the hammers are very grooved, this can result in an unevenness of tone that wasn’t there before, so this has to be done judiciously. If tonal discrepancies are a problem, toning can be employed, (sometimes in conjunction with filing of the felt) that is, softening the hammer felts with a needling tool in order to even out the tone. This is an important part of piano maintenance and also of preparing newly manufactured pianos for retail.

Equally important is the spacing of the dampers, particularly in the middle and upper sections where the damper felts are flat. If the felts deviate at all from central they can become distorted and, eventually, inefficient. I would say that there is some element of this problem in every piano I see and I make a point of doing what I can to correct it. The dampers' lateral positions can be altered by bending the damper wires.

Another frequent task is the tightening of action screws. These can become loose as a result of excess dryness and it is sometimes the case that all the screws need tightening. Loose screws can cause audible clicks and rattles.

If any of the action parts are working too slowly, they can often be persuaded to work properly with lubrication; I use Protek liquid polymer to ease action parts.

Lastly, I will always ensure that the piano pedals are working correctly. The "soft" pedal on an underdamped upright piano is more or less redundant, in that its operation actually has a deleterious effect on the touch and I will sometimes decommission it. The correct functioning of the sustaining pedal however, is important and there is usually something to do to ensure that it works properly. 

You can read about more serious piano problems in the section on this website about repairs.