Tomatoes are best grown in either a greenhouse or a warm conservatory. That said, they can be grow outdoors and there are varieties more suited to outdoor growing.
Sowing Seeds
I tend to sow multiple seeds per 4 inch pot of seed compost and place on a warm windowsill or in a heated propagator.
Keep the compost moist but not wet and once the seeds have several sets of leaves you can transplant them into their own 4 inch pots.
Transplanting
I like to wait until the plants are almost root bound to a 4 inch pot before transplanting either outside or into larger 10 inch pots.
If planting outside you must wait until after the last frost.
Plant Care
As the plant grows, tie the main stem to a sturdy cane, or provide a cage to offer support. Water and feed the plants regularly, you must keep the soil moist to avoid problems like splitting fruit.
As the plants grow some people like to restrict the fruit per plant, some experimenting might be needed to find what works for each variety to get a good crop.
Harvesting
Harvest the fruit when ripe and fully coloured, harvest with a sharp knife to avoid plant damage.