Percussion is the oldest form of instrumental music by a long way. The thousands of different percussion instruments we have today evolved from the early rattles, drums and pitched sticks that were the earliest members of the percussion family. Because there are so many different types of percussion instument, it is very important to treat them as individual instruments and not as one massed group.
Percussion instruments have been classified into two main groups, idiophones and membranophones. Idiophones are vibrating instruments, subcategories of which include: concussion idiophones such as castanets and clappers; percussion idiophones like marimbas and triangles; scraped idiphones such as the guiro; shaken idiophones which are different kinds of rattle; plucked idiophones like the jaw-harp and mbira and friction idiophones like the glass harp. Membranophones are instruments with a vibrating membrane, which can be further subcategorised into tubular drums, into which category fall most modern drums, and kettle drums, which are made in an elongated half-sphere shape with one membrane. Not all membranophones are percussion instruments - the kazoo is technically a membranophone.
The best way to take care of a percussion instrument is to research its background and play it regularly. Research its history and find out what kind of climate it was designed for. If this matches the climate you live in, your job is easy. If the instrument was designed to be played in a much hotter or more humid climate than your own, you may find that you need to simulate this climate as far as possible in order to keep the instrument at optimum playing level. For example, percussion instruments from the Balinese gamelan have evolved to suit the Balinese climate, which is hot and humid. They are made of jackfruit wood, bamboo resonating tubes and brass or iron keys. If exposed to the cold dryness of a British autumn, or even the very dry heat of summer, with no regulation of their immediate conditions, the bamboo will dry out and split, causing buzzing on the split notes and an unpleasant tone. The bamboo will change in volume as a result of this drying, and will not fit properly into its jackfruit wood frame. The instruments can be just as easily damaged by neglect as action. A little research into the conditions the instrument was designed for can go a long way to prevent it becoming damaged and unplayable.
For hand drums of every kind (excluding tabla which need very particular care) regular playing and ensuring they are kept tuned is sufficient to keep them in condition. The oils from your hands will keep the drum skin supple - you may notice that after a prolonged playing session your palms and the working parts of your hands take on a silky dryness. This is caused by the drum skin absorbing the oils from your skin. It also sloughs off quite a few dead skin cells along the way! If your hand-drum skin feels unusually dry and it is skinned with real hide, you could try moisturising your hands before playing with an unperfumed oil like baby oil. Make sure all the oil is absorbed into your hands before playing - the drum skin will absorb it more evenly if it is well absorbed into your skin first. Don't ever try this with a synthetic skin or you could wreck it - double check that it isn't just a good imitation of real skin by looking at any stamps on the skin - stamps on real hide will bleed their ink slightly whereas on synthetic skins they will have sharp edges. If the skin has a name - for example, Remo Fibreskyn - it is likely to be synthetic hide.
Drums with metal tuning lugs from other countries may use a different shaped nut from UK ones. Normal UK nuts are 6 sided whereas on Cuban congas you will find 5 sided nuts, and so on. Don't try to tune drums with pliers unless you have to as it could smooth the corners of the nut, making it more difficult to gain purchase. Use a tuning key in the right size from the appropriate country.
Relatively modern designs of percussion instrument like the xylophone or drum kit tend to need very little day to day care. If they are broken, obviously you need to have them mended by a professional as soon as possible As to keeping them in condition, they have been developed to need very little care beyond tuning. If you're buying a drum kit (depending on individual specifics) it may be worth immediately changing the factory - basic skins for a better set, and keeping the originals as spares. Drum kit manufacturers towards the upper end of the market often make good skins, but lower-end models can be substantially improved by the addition of a set designed by a company which specialises in skins. If you never need the spares, and you end up selling the drum kit, put the original skins back on - you could gain value on the usual second hand price because it looks factory - fresh.
Remember, when you buy your instrument to begin with, ask the retailer about care. If they don't know, or you get the impression they don't know as much as they think, ask them to put you in touch with their supplier. Somewhere along the line you will be able to get precise instructions for the care of your instrument, and this work could considerably extend its life span.