Place four to six medium to large green tomatoes in a paper bag. I use sacks that are a little larger than a school lunch sack. If you have a fullsize store brown paper bag, you should be able to ripen up to 12 tomatoes inside.
Place 1 to 2 bananas inside - depending upon the size of the sack and the number of tomatoes. For the size of sack and number of tomatoes that I use, one banana should do the trick. Do not place too many tomatoes inside because doing so can bruise them and facilitate rot.
Roll the sack down tightly towards the tomatoes and tape or staple together to prevent it from opening back up and to decrease air flow.
Put the paper bag in a cool and slightly humid place for up to two weeks.
Check the progress of the ripening tomatoes every few days to ensure no rot is occurring and to see if the banana needs replaced with a fresh one.