I recommend purchasing the Professional Tuning Kit TM w/ satin rosewood handle from International Piano Supply (PianoTuningHowTo NOTE: please don't go to pianosupply.com for they have closed and somebody got the domain name and put a very dangerous website). Each kit includes a professional-quality rosewood, non-extension tuning hammer, 8 rubber mutes (2 wire-handled), a tapered temperament strip, and professional quality A440 tuning fork. Most tuning kits for sale elsewhere are more expensive, are of lesser quality, and often include tools which are unnecessary clutter to a beginner.
Please note – the quality of the tuning hammer is vital to the success of anyone attempting to tune a piano. Any low-cost beginner’s hammers I have tried were very difficult to control. A gooseneck hammer is about as useful for tuning as a real gooseneck! A quality tuning hammer needs good weight and balance. The hammer included in this kit I have tried with good result. Using a hammer of lesser quality is courting frustration. Spend a little extra and buy something that will do the job properly!
Rubber mutes – I know some tuners who use up to a dozen rubber mutes, in addition to the temperament strip. I generally only use two 6-inch tapered rubber mutes and one wire-handled mute to insert the temperament strip and to reach places in the high treble where space is tight.
Glue and liquid graphite – I keep these in my tool case, but usually need these two items in small quantities. I emptied two fingernail polish bottles and filled them with PVC-E glue and liquid graphite. The brush tips in the bottle covers are great for applying both evenly.
The following is a list of tools I use infrequently, but when I need them, they are essential and irreplaceable:
The mother of all screwdrivers, aka Big Bertha – I’m a big fan of using tools which are ridiculously overqualified for the job. For tight screws, this is the best tool I’ve used. Try using the standard plastic-handled screwdriver from Sears on a tight keyblock screw, and your hand may never work right again! Big Bertha is a professional quality electricians’ screwdriver which took me several months to find, and has been well worth the cost. (PianoTuningHowTo NOTE: you can also use a big screw driver that has a square rod so you can tighten with a wrench)
Damper guide rail bushing tip – This is the permanent solution to swollen damper guide rail bushings. I had this tool machined to fit into an electric key bushing iron. I’ve encountered several pianos with which this tool has saved me many hours of labor.
Digital hygrometer – This is useful to use as a reference for humidity-related issues. I recommend that my customers buy a digital hygrometer from Radio Shack to monitor the humidity changes where the piano is located.
Small ‘C’ clamp – attach to side of tool case and !presto! - instant bench vise.
For those who dabble in the dark arts of repairs that “just keep it going” (see the need to improvise), here is a short list of materials to improvise with: wooden matches, extra hammershanks, masking tape, a hacksaw blade, 6” lengths of heavy gauge music wire (size 18), center pin lubricant and hypo-oiler, other tuner’s business cards, extra screws of varying size, and an extra temperament strip to cut.