One of the most important factors influencing piano tuning stability is humidity. A piano humidifier is therefore an essential investment for all piano owners.
As a rule of thumb, your piano's humidity should be about 50 percent. More specifically, between 50 and 55 percent is ideal. A little more or a little less is acceptable, with too little being by far more harmful than too much (assuming it isn't raining in your living room). Anything below 40 percent is reason to hit the panic button, since extremely dry air could cause the critical soundboard to crack. (It goes without saying that you should never, ever place your piano directly in front of a heater.)
By contrast, on a rainy day humidity might go all the way to 70 percent, but this won't ruin your piano; it will only "retune" it.
Every piano owner should pick up a hygrometer and leave it directly on the piano. This tiny device can be found in hardware stores for not much more than the price of a cup of coffee.(By the way, never place a coffee cup on a piano! I panic when rehearsing with singers who automatically set their water bottles on the piano. At my university someone once completely ruined a $100,000 Steinway concert grand with a 50 cent can of Pepsi. The culprit was never found.)
There are essentially two ways of guaranteeing proper humidity for your piano: external and internal. An external solution is both easiest and cheapest, although it is less accurate. You need no more than an ordinary room humidifier, and you probably only need to turn it on during winter. It's important to keep the humidifier slightly away from the piano; it shouldn't be directly underneath a grand or shooting its stream directly onto your piano. I keep mine a couple feet from the piano, pointing out into the room.
A more sophisticated solution is a dedicated humidifier to be built directly inside your piano. There is one company, called Dampp-Chaser, that has manufactured piano humidifiers for many decades. These are a serious investment at between $500 and $800 (US), and they need to be installed by your piano technician. If yours is a "mission-critical" piano or a room humidifier does not solve your piano's humidity issues, having the Dampp-Chaser piano humidifier system installed will prove to be a worthwhile investment.
My personal recommendation is to start with a hygrometer and room humidifier and monitor your room's humidity. This will suffice for most setups.