I harvest some of my green tomatoes yearly before the frost, hoping they'll ripen indoors, but they never do. I usually place them in the sun on the window sill but eventually throw them out. How can I successfully ripen them this year?
Leaving tomatoes out to ripen in the open air doesn't work, as you've found out.
You ripen tomatoes off the vine in a shallow plastic or cardboard box with a lid to create a simple ripening chamber.
The bottom of the box is lined with a one-inch layer of newspaper, and you place the green tomatoes next to one another, but don't let them touch each other. A second layer can be added, separated with another layer of newspaper, but no more.
The box is then placed in a cool, out of the wary the way location like the garage. Every five to seven days, you open the lid a remove those that have turned red.
The chamber traps the ethylene gas naturally given off by the tomatoes. You can hasten the ripening by adding an apple or other fruit that releases ethylene. I know an old-school method would have you wrap each tomato separately in a newspaper or other material and store them in a box. I think it's tedious, and the lid makes that unnecessary.
You should select tomatoes that haven't been damaged by the cold. So, it may be too late for this year, but I'd still try a few anyway to get a feel for the technique.