Restoring an upright piano requires patience, work, knowledge and the proper tools. It is possible to completely restore an upright piano without having a professional do the job, but a few critical factors need to be taken into consideration.
Play the piano. Hit every key on its own to see if it makes a sound or works at all. Ignore the tuning for the moment and focus on mechanical issues. Note if there are keys missing. Check if the pedals work or if they are stuck, broken or disconnected. Look at the piano cabinet and note down any scuffs, scratches and holes. Write down problems you notice, and be specific (which keys are missing/not working), to help you during repair.
Open the piano lid. Depending on the piano you have, this could be as simple as lifting the level board up (with most Baldwins), or it could be more complicated. You may need a wrench to loosen nuts in the back of other piano brands. Remove debris that may be in the piano; make sure not to throw away pieces that actually belong to the piano, but may have broken off (such has hammer heads). Number the keys from left to right--it will help keep order if you need to remove them.
Fix the areas of the upright action that need attention. The action is a complicated structure that is the mechanical skeleton of the piano sound, hammering the string on the soundboard when you play a key. Find a solution to any problems with the action without removing it, but if removal is necessary, take it in stride. Disconnect the pedals from the action, and remove the screws holding the action in place. Make sure not to lose any parts--mark them to put them back into place later. Use both hands and hook your fingers through the metal braces in the centre of the action, and slowly lift up and out.
Start repairs by fixing or replacing missing parts (keys, hammer heads, screws, pedals). Upright pianos use hammers connected to the keys to strike the string, so check for connection problems, making sure that all the parts exist, are in place and connect to each other. The pedals should be connected to the keyboard by sticks, and if any are loose or broken, they will not work. Tighten loose pins. After the action and musical portion of the upright are repaired, begin work on the cabinet. Dust, polish or buff out scratches in the wood. Replace cracked or fragile wooden legs, tighten any nuts or screws that may be loose.
Stay aware of the delicate nature of an upright piano. Upright piano restoration can be enjoyable, difficult, expensive and exciting. Understand that piano restoration is not cheap or quick and some parts (like a cracked soundboard) may be almost impossible to restore yourself. Replacement parts can be expensive.