As Gardeners we wonder why plant freaks buy vegetable seeds for a lot of money. This is much cheaper by going to a discounter, buying the tomatoes that taste best and keeping the cores! If it isn't accidently an over bred variety, you can grow your own good-tasting greens.
This also works with other fruits or vegetables that are sold including their seeds. Melon, pumpkin, avocado, citrus and so on. Partly the cultivation of special plants requires a special procedure, but with tomatoes the success is guaranteed. The ones who have a (very) sunny window can also breed in the apartment. From about the end of February you may begin. Then the plants will have a reasonable size to set them into the open, until frost-free spring.
For this you just take a really ripe tomato and cut it in half. The slimey cores only need to be collected. This is done best with a handkerchiev or paper towel, because the gelatinous layer around the core must be removed with it. The reason ist because it inhibits the germination. Then the seeds should be dried for a few days. After it they are ready to be planted. However, dried Tomato seeds can still germ after years.
Especially for the germing from seeds you should buy special potting soil. It differs from normal potting soil because it has less in nutrients (especially nitrogen). The sense is, that the seedling is forced to produce many roots at the beginning and does not grow too fast. Like that you get a vigorous plantlet. A handful of dirt from anywhere is suitable as well. Fertilized potting soil is not!
Now simply fill a pot or planter with this nutrient-poor soil and put in the cores with a few centimeters distance to each other. Then cover it with about 0.5 cm of soil and carefully pour some water on it. If you keep the whole constantly moist, you can admire the first green seedlings after a few days. From about May (depending on the region), if no more frost must be expected, the small plants can be planted outside.
Tomatoes need a lot of light for a good harvest. On a sunny windowsill or balcony they get also ripe, but it is much better when they get sun all day long. Small tomato plants are offered in many supermarkets in the spring. They onlycost a few cents, but it reduces the fun-factor of growing something own just from the bebinning ;-)
Garten trick :
When the tomatoes have formed fruits it is time to "break them out". Because a tomato plant will also form supplementary shoots between the leafs and the stem. So the force is not wasted for the formation of additional leaf green, but is completely used for the fruits.