Follow this method if you do not have a food dehydrator. If you want to safely store dried tomatoes long term, you should probably use a dehydrator.
3-4 pints cherry tomatoes
Large baking tray
Highly porous cloth like nylons or window screening
Very warm, sunny location
1. Chop all the cherry tomatoes in half and place on baking tray with cut side up.
2. When tray is full, place in a sunny location like a sun room or south facing window. We use our prop house as it keeps the dew off.
3. Cover the tray with porous fabric to keep flies and yellow jackets off. We use an agricultural fabric called Proteknet that we also use in our fields!
4. Place an oscillating fan directly over the trays, so it blows over them. Depending on temperatures and ambient humidity, the tomatoes should be dry enough to use within 3-4 days.