Saving heirloom tomato seeds for next year's garden is super easy. We do it every year and have great success with it. It's important to save only heirloom, not hybrid tomato seeds because hybrids won't produce true in the next generation. We select the very best specimens of each variety while they are still on the vine. You're trying to replicate, so make sure you're replicating the very best. I usually pick them at ripe then further kind of over-ripen them on my windowsill.
The first step is to remove the seeds along with the jelly stuff that surrounds them. I put it all in a clear water glass and throw out the remaining pulp and skins. If they're not too over-ripe, you can have a snack!
Pour about a half cup of water on top of the seeds and put them on your windowsill. Leave them for a couple of days to ferment.
This is what the seeds/water mixture will look like when it's fermented, stuff rises to the top of the water. This is the yucky part. I get in there with my fingers and squish what is floating around so the seeds fall to the bottom of the glass. Carefully pour off the water and yucky stuff and add some more fresh water. I let this sit for a half hour or so then pour the water off of the seeds again and replenish it.
Keep refreshing the water until you get what you see in the glass to the right. Basically seeds and clearish water. If any seeds continuously float to the top, go ahead and get rid of them. No need to waste any effort next year trying to grow bad seeds.
Take a strainer and pour the entire glass of water into it and give them a rinse under running water.
Dump your strainer onto a piece of newspaper, spread the seeds out so they are in a single layer then put it aside and forget about it for 2 weeks. At that time, the seeds will be fully dry and ready to be stored until planting time again. Happy gardening!