First steps
Carve into the center and opened one a quality tomato so that you can retrieve the seed.
Squish out the seed and put them into any upcycled container with a lid.
It's best to take seeds from several of the same variety of tomato for genetic diversity within that variety. Bear that in mind when you're harvesting tomatoes for seed and take several from each plant.
It's also important to pick your best performing tomatoes for seed saving. So, when you're planting, plant a few of each variety from which you want to save seed just to have a good mix. When it's time to harvest, pick the tomatoes with the characteristics you desire in future tomatoes.
Next Steps
Look around the outside of the cut tomato for any scars, squishes, or cracks and carve them off.
Place the impurities you carved off into the yogurt container with the seeds.*
Squish all the liquid from the tomato on the cutting board into the container.
Add enough water to cover the seeds.
Secure the lid (just so that smell the coming fermentation process didn't escape - it's not pleasant).
Label the container and attach a future seed envelope to the lid so that all the information for that tomato variety is right there, taped to the container. Labeling is SO important!
*These blemishes have the bacteria you want for fermenting tomato seeds. Yes, fermenting! Fermenting tomato seeds is a necessary step in successfully saving them.
Tomatoes have a gel sac around their seeds that is meant to protect the seed until the next season when it's time for them to germinate. In nature, that gel would be broken down and the growth inhibitors would dissipate after the tomato had sat and decomposed through the winter.
Fermenting the tomato seeds in the yogurt container just mimics that process and keeps your seeds healthy.
Final Steps
Put your seeds somewhere warmish and safe on a counter or shelf.
Swirl them gently every day and check them to watch for signs of mold.
Once the seeds have developed a nasty, gloppy mold at the top that covers the width of the container, they're ready for final processing. This takes around a week, but it really depends on how warm it is in your house.
At this point, transfer the contents of the seed container into a small bucket and add some water.
Let it sit for a minute so that the mold layer and tomato bits rise to the top, and then dump off the top, yucky water.
Repeat this process, adding clean water again when you're done. Let them sit to settle again, and then swish the seeds and dump off more gunk. Repeat until your water is clear.
Drain the seeds and lay them to dry on a paper towel or coffee filter. Allow to dry for at least a week and ruffle now and then to move around.
Healthy, viable seeds will sink. The useless ones will float to the top where you can just skim them off and dump them. If you ferment your seeds too long, they'll start to germinate in the container. So, be sure to keep checking the seeds and process them as soon as they're fermented but not sprouted.
A sprouted seed can be immediately planted, if you'd like to try growing a tomato indoors this winter. Or, it can be discarded.