Wash and ore your tomatoes, then set the aside. Make sure you don't prep more than you can fit into your dehydrator in a load.
Slice your tomatoes as thin as you can (to reduce drying time), but most importantly make sure your slices are as uniform as they can be.
Place your slices either directly on your dehydrator trays, or onto silicone liners, depending on your machine. I find they dry faster directly on the trays, but they also stick more, which is why the liners are helpful. Make sure the slices are single layer and not overlapping.
Dehydrate your tomato slices at 135 degrees for anywhere from 6-12 hours, depending on how thick/thin your slices are. Flipping your tomato slices halfway through will significantly reduces your drying time and help them dry more evenly.
Check your tomatoes frequently to check for dryness. Fully dehydrated tomatoes should feel dry and leathery, slightly crispy. If they're turning a dark color or overly crispy they might be overdone. If they're soft or still feel moist at all, they're not done yet.
Make sure your tomatoes are completely cool before sealing in an airtight container. Any heat left in the tomatoes can lead to moisture building up, which can allow them to go bad.
Condition your tomatoes for about a week by vigorously shaking them every day. I like to use a half gallon jar for this, filling it only 1/2-3/4 full to allow room for shaking. Conditioning is a really important step in the dehydrating process, so don't skip this step. Almost 100% of the time when I hear of someone being discouraged with their dehydrated food, it's because they didn't condition it properly after dehydrating. See more about conditioning below.
Store your dehydrated tomato slices in an airtight container indefinitely. Especially if you're planning on storing them super long-term, check them every so often to make sure there's no signs of moisture or mildew.