The above advice is correct, but keep firmly in mind that, excepting pears, none will develop the true flavor and texture of tree ripened fruit. Pears, oddly, improve in flavor and texture when ripened as described, or merely on a window sill.
It is claimed that adding an apple to a paper bag of unripened fruit will help - the apple emits ethane gas, which is used commercialy to ripen fruits, etc.
I find that giving close attention to the "feel" and aroma of fruis in the store can result in bringing home better quality - often even fullly riipe. Thisworks especially well if you know when the store receives the fruit, and be among the first customers to purchase it.