Tomatoes, like peaches, are one of the many fruits and vegetables that will continue to ripen after they've been picked. They won't ripen quickly and the won't usually ripen perfectly, but under-ripe tomatoes can be improved upon.
As they ripen, tomatoes and other botanical fruits let off ethylene. The more ethylene they're around, the more they'll ripen. So putting all of your under-ripe tomatoes together in a breathable container - cardboard box, paper bag, plastic bag with holes cut in it - will help them ripen by capturing the ethylene they let off.
Note that using plastic contains too much of what they let off; in-tact plastic bags and containers will trap in humidity along with ethylene and humidity will make tomatoes rot more than ripen.
Check the tomatoes regularly and remove them as they ripen. They are unlikely to ripen at exactly the same rate, so check each tomato by taking it out of the bag, feeling if it feels heavy for its size, looking at its color, and smelling to see if it smells like a ripe tomato.
If you want to speed things up, add a ripening banana. Bananas let off more ethylene than other fruits, so they help their brethren along the ripening path.
Once your tomatoes ripen, store them on the counter. Never refrigerate tomatoes; temperatures under 50°F turn them mushy.If you need to keep them longer, better to pop them in the freezer. Learn more About Tomatoes here.