Peaches, like apples and pears and avocados and tomatoes (among other fruits), can ripen after being picked. This comes in handy both because if you accidentally end up with unripened peaches, it's nice to know that they can be saved and because you can purposefully choose peaches at different levels of ripeness with the plan of ripening the harder ones to eat later. Below you'll find three ways, each with its own speed, to ripen peaches once you get them home.
The Easiest Way
The easiest method is simply to leave peaches on the counter. Peaches like best to be kept on their shoulders (not their bottoms) and not touching one another. That may not work for your kitchen, and putting them in a bowl isn't the worst thing in the world, just handle all peaches gently and don't stack too many on top of each other.
To speed this up, you can leave them where they will receive some direct sunlight, as long as that spot doesn't get too hot and start baking them (which will give them mushy spots).
The Fastest Way
If you want to speed things up, pop the peaches in a paper bag. It will contain the ethylene gas the fruit gives off, which hastens the ripening process. Pretty cool, huh? Want to speed things up even more and ripen them faster? Add a banana in there, too, for even more ethylene action.
Place Them in the Fridge
When you want to vastly slow down the ripening process, put the peaches in the fridge. Cold slams on the brakes of the ripening process, but doesn't bring it to a complete screeching halt. Keep your eye on any peaches you relegate to the fridge; if left in there too long they can start to dry out.
Once you have perfectly ripe peaches you should eat them. Many people find it's best to store peaches that are ready to eat out on the counter so everyone can see them, think "wow, that peach looks like a delicious snack," and eat them immediately.
Seriously, visible fruit is eaten fruit—keep ripe and ready fruit where you can see it, remember it, and eat it in its prime.
If immediate consumption isn't in the cards, peaches can, as mentioned above, be stored in the fridge instead, where they'll last nicely for a few days. Anything longer than that, and think about taking a moment to do something very easy that will keep those peaches around for months and freeze them.
Frozen peaches are fabulous additions to smoothies, work in any baked good, such as peach pie, and can even be used later, when things aren't quite so hot out, to make peach jam or peach chutney.