One caviat, this will not work with seeds from a hybrid tomato which will not produce the same fruit as the parent. If you want to grow hybrid tomatoes, you're better off buying seed from a reputable seed supplier or simply buy the plants at a garden center in the spring. An online search of your tomato will confirm if it's a hybrid or an heirloom variety.
At the farmers' market last year, I found a delicious, new (to me) tomato. A larger-than-average, dark, purple-red cherry tomato. After looking online, I assume they are Chocolate Cherry tomatoes, however, there is also a Black Cherry, Black Pearl, and several other dark red cherry varieties. They were so tasty and larger than the average cherry tomato so I wanted to try and save some seeds to grow my own. This is what I learned and what worked for me after talking to a chef who saves tomato seeds and grows his own vegetables for his restaurant...
The first step is to pick the very best tomatoes from which to save seed. You don't want to use under-ripe or over-ripe tomatoes. Of these three, similarly ripe tomatoes, I chose the biggest one on the far left from which to save seed.
Then, cut the tomato in half around the 'equator' of the tomato.
Squeeze the seeds, or scoop them out with your finger, into a glass jar to which you've added about 1/3 cup of water. Don't worry if some of the pulp goes in too. The reason for putting the seeds in water is to get the gelatinous coating off of the seed that could prevent them from germinating when you plant them. I've read that filtered water should be used but I used regular tap water with no problem.
Cover the jar with some plastic wrap and make a small hole in the top with a sharp knife for aeration. At least twice a day, for the next 3-4 days, give the jar a few gentle swirls back and forth to help remove the coating from the seeds.
By day 3 or 4 you will may find mold starting to grow inside the water or on top of the water. That shows that the process is working. The good seeds will have settled to the bottom of the jar. If you have any seeds floating on the top of the water, don't save them because they are bad. Also, don't keep the seeds in the water any longer than 3-4 days because they may start to germinate!
Gently, pour as much water out of the jar as you can without pouring out the seeds. Then place the seeds into a fine mesh strainer and rinse thoroughly, swishing them around with your finger.
Dry the seed on a piece of paper toweling or on a paper plate. I found out that seeds will stick to paper toweling but I just pick them off with my fingernails. In about two days, when the seeds are completely dry, put them in a small, paper envelope marked with the name of the seed and the date and store them in a cool, dry place over the winter. I keep them in a cabinet inside the house along with other seeds that I save over the winter.
Early next spring, about 8 weeks before your area's safe outdoor planting date, you can start the seeds in containers indoors. I like to use vermiculite as a planting medium which I find at my local garden center. All you need is a sunny window to keep the seedlings happy until they are planted outdoors.
Growing tomatoes from seed is fun and deliciously rewarding! All they need is sun, lots of water and fertilizer, especially if you are growing them in a containers. You must also be prepared to support them somehow. This one is growing in a container next to our back porch and has climbed all the way to the ceiling with the stems tied to the post with soft garden twine.
Good luck and happy seed saving!