How long you brine for depends on the concentration of your brine and thickness. If you do an "equilibrium brine" like others have suggested, it could take 3 days sitting in the brine to get to the right concentration. If you make a ridiculously strong brine, then you may only need to let it sit in the brine for an hour, but then it should sit for a while (minimum time depends on thickness) so that the salt can distribute itself evenly - otherwise, you'll have a salty ring on the outside, and unseasoned meat on the inside. Once you take it out of the brine, the salt will evenly distribute itself over time - the longer you let it sit, the more even it will be. Once it is completely even, letting it sit longer won't hurt it (until the meat spoils!).
If you have several days before you want to use it, the equilibrium brine is best because there is no way to oversalt it. Once the salt in the meat gets to equilibrium with the surrounding brine, it just sits there, no worse for wear. The problem with using a strong brine is that the meat will continue to take on salt until you remove it from the brine - the longer it sits in the brine itself, the saltier the entirety will be.