Harvesting pears is a little different from most fruit in that they must be picked before they are ripe.  If they ripen on the tree they ripen from the inside out so the inside becomes mushy before the outer area is ripe.  Pears should be harvested when fully formed, but not ripe.  Most years that time is early August for Bartlets, but this year everything seems to be early, so it's important to watch your pears for when they are mature. 

After harvest pears should be cooled for a couple of days at least.  To ripen them bring the temperature up to 65-75 degrees.  They should ripen in 4-5 days.

Here are two articles on picking, storing and ripening pears, When to Pick and How to Ripen Pears to Perfection and Picking and Storing Apples and Pears.

Thank you, Anne, for your response. That was helpful. But I would still request one additional piece of information to help me do the best job of not wasting the Bartlett pears I am growing. How often should I perform the gentle lift test to know when the fruit is ready to harvest? I agree with your advice about waiting too long and having the fruit turn mushy from the inside. So it is still not completely clear about how I know when to pick the fruit successfully. Also, I am getting what is called "June drop"--with some fruit dropping off the tree. I was told that this may be an effect of incomplete pollination. These pears that have dropped are large (some appear to have been pecked by a bird or nibbled by a squirrel near the top of the fruit). Can I chill these and see if they will ripen? Or should I just compost them? Thanks, Michael

Developing a feel  for when to pick a pear will take a bit of trial and error, because the changes are subtle.  There are four basic ways to determine maturity of a pear:  1.  size and shape (should be that of a ripe pear) 2.  color, check every couple of days and when the color yellows slightly it's ready 3.  feel, a slight softening of the texture from very hard to firm and 4.  ease of picking, pears should twist off, as you know.  I would try a few pears you think are right, cool them for a couple of days, then ripen and see how they develop.  You can certainly try that on dropped fruit - what have you got to lose?  Once you have a method you can chill pears and ripen them at your pleasure.