Wash the tomatoes and drain well.
Slice each tomato in half lengthwise.
Arrange the halved tomatoes on your dehydrator trays with the skins facing down. This will prevent the juices from dripping. Leave a bit of space between each tomato so they are not touching. Sprinkle with oregano and sea salt if desired.
Put the trays in your dehydrator and turn it on. If it has a thermostat, set it between 125º to 135º.
It will take 10 to 12 hours for the tomatoes to become "moist dry" and will take 12 to 14 hours to become "leathery dry." These are approximate times. Periodically check the tomatoes for doneness, and rotate the trays. Even if your dehydrator has a fan, rotating the trays will help them become more evenly dried.
Once dried to your preference, let the tomatoes cool down. Place them in an airtight glass jar with a screw lid; label with the date.
Leave the jar at room temperature for 24 hours so the moisture content of the tomatoes will become more evenly distributed. This process is called "conditioning".
Store moist-dry tomatoes in the freezer. Store leathery-dry tomatoes in a cool, dark, dry location.