Growing tomatoes indoors will give you your own lovely, sweet tomatoes that you can enjoy in salads and other meals. Tomatoes are relatively easy to grow and so useful and rewarding. I've provided all the advice you need to get started on this page.
There are a number of varieties of tomato. Heirlooms (e.g. black krim) are tomato varieties that haven't been artificially bred into a hybrid. They tend to taste better but are more susceptible to disease.
Some tomatoes are easier to grow than others. I'd recommend trying these smaller varieties for your first attempt at growing tomatoes indoors.
A tomato plant will do well in a 15cm (6") pot containing one plant. Don't restrict yourself to ordinary containers -- have you thought about using a hanging planter for your tomatoes? Use a good quality general-purpose potting soil.
Growing from seeds has the benefit that you generally have a bigger choice of varieties to plant. It does mean you need to wait a little longer. Sow the seeds 5mm (1/4") deep, preferably in little seedling trays to get them started. Once they've established themselves, transplant the seedlings into a pot.
Buying seedlings from your local nursery is the easiest way to get started. Make sure you get a variety that is suitable for growing indoors in the space you have available. Water the seedlings for a day or so and then transplant them into a larger container. It's a good idea to put a stake in the pot to support the plant, especially when it starts bearing fruit.
Tomatoes are naturally pollinated by insects or the wind which moves the pollen from the anther to the stigma of the same flower. Neither of these is likely to happen indoors. So I'd recommend giving your tomatoes a light tapping on the stems on a daily basis once flowers develop.
In nature, a bee would grab onto the flower and beat its wings to release pollen. One way to simulate this is to use an electric toothbrush to produce similar frequency vibrations. Hold it against each branch for a couple of seconds. The tapping-with-your-hand approach also works if you don't want to use an electric toothbrush.
Using hydroponics you grow your tomatoes in water containing mineral nutrient solution rather than soil. Your tomatoes will grow quicker and larger than in soil. Putting together a hydroponic setup is more involved than planting with soil, but with a little reading and effort, you should be well on your way to lovely red hydroponic tomatoes.
Tomatoes like full sunlight, so the windowsill is the perfect place to put your container. If you're using artificial lighting, I'd recommend 12-14 hours of light per day.
You should fertilize your tomatoes regularly. In the early stages, tomatoes like more Nitrogen, so use a plant food with relatively more Nitrogen to start with. Once flowering starts, switch to a fertilizer that is higher in Phosphorous and Potassium. Fertilizer with an NPK of 5-10-10 is often sold as tomato fertilizer.