Buy the largest and ripest tomatoes that you can find. Rinse and chop into fairly small pieces. The smaller they are, the quicker they dry.
Lay them out on a large tray and sprinkle with salt. Cover loosely with the cloth and leave out in the sun during the day. Bring the tray back in at night and refrigerate until the next morning when you take it back out. Repeat for a few days until they are completely dry to the touch and have shriveled up significantly. (I live in a really hot place, and mine took 5 days.)
Once dry enough, store in a jar in the fridge for up to 2 months. Alternatively, pack them in a jar, cover with olive oil and refrigerate.