What is the best way to ripen fruit at home?

Lately at the grocery store, they’ve been selling really sour fruit. Usually, it ripens alright, but recently, the plums and peaches I’ve bought have actually gone rotten and mushy while they still tasted unripe.

I’m not sure if I’m doing something wrong, but if people could tell me the best way to make sure fruit ripens before it goes bad, perhaps I could troubleshoot or try something new. I hate wasting fruit.