In a good tomato year I have way too many to eat fresh. To store my excess, I freeze lots of them. I make tomato sauce and either can or freeze it, but probably my favorite thing to do with tomatoes is to dry them. Drying or dehydrating fruit or vegetables can concentrate the flavors and the texture becomes very chewy or even a little crunchy, depending on how long you cook them.
I use a dehydrator, which I love. I simply wash the tomatoes and cut them into as uniform pieces as I can. For cherry and plum tomatoes, I just cut them in half. Larger tomatoes, I core and then cut into quarters. Whatever the size, I put the pieces on the sheets that come with the dehydrator and turn on the machine at 125-135°F and leave them to dry for 12-24 hours depending on the size of the pieces. I know they are dry when they are shriveled and leathery feeling. Sometimes I take them out when they are still a little soft, because they are particularly delicious and have a silky texture at this point.
It's nice to have a dehydrator but an oven will work too. Cut the tomatoes as suggested above and put them in roasting pans. It's a good idea to line them with parchment, because otherwise the tomatoes can stick and be pretty messy. Cook at a low temperature until the tomatoes look dry.
Some people sprinkle the tomatoes with salt and pepper, even sugar, before drying, but I don't put anything on them and they are delicious.
I have two ways to store dried tomatoes and I usually do some of each. For a rich treat, I put the dried tomatoes in a small mason jar with good quality olive oil. These will keep for about 2 weeks in the refrigerator, or I freeze them. I also just put some dried tomatoes in a jar without the olive oil and freeze those as well.
I serve the dried tomatoes in oil with cheese and crackers (they are particularly good with chevre) or put them on top of green salads. Or sometimes I just snack on the plain dried tomatoes.
Small jars of the tomatoes, simply tied with raffia, make great gifts.