Tomatoes are easy to get started from seed. Place two or three seeds into a small pot filled with fine compost, cover the seeds with a light sprinkling of compost, and they will germinate quickly provided they are kept warm and covered (with polyethylene or propagator) until they have germinated. Tomatoes need a temperature of around 21 C to germinate.
There is the question of when to sow tomato seeds, which in part where in the UK you are growing your seeds. The growing season for tomatoes varies a little depending on where in the UK you are growing your crop. The season is longer in the country's south, where you can often germinate from seed as early as late February, with good light conditions and grow through until around late October/early November. Further north and in areas where there is more cloud cover, the light is less good and it may be prudent to delay sowing seeds until mid to late March. Tomatoes need good light and heat to grow well.
Early in the year when conditions are cool, it is essential to germinate tomatoes in a warm place and preferably with a moist atmosphere such as in a propagator. The seedlings will emerge after a few days and once the seedlings emerge, uncover and reduce heat. Seedlings (of any plants, not just tomatoes, ) left for too long in a propagator can become will be floppy. It is important as soon as the seedling has fully emerged to remove the pot from the propagator and keep frost-free.
When deciding a variety of tomatoes to grow from seed, think about the size of the tomato. The large beefsteak varieties will need a longer, sunnier growing season to ripen than the smaller cherry type. This means where in the country you are gardening may be an important factor in deciding which type of tomato to grow. This is particularly true of tomatoes gown outside as opposed to in a greenhouse which provides a more sheltered growing environment.
As with all plants grown from seed, Tomato seedlings can become leggy if light levels are poor, which commonly occurs when seeds are sown early in the year. This is because the seedlings stretch towards the light, and if the seedlings are in grown in conditions where the light is uneven, or low light conditions, it will produce poor seedlings for potting on. Early in the year tomatoes grown inside, and in particular on a windowsill, can easily become leggy. If you do grow on a windowsill where the light is predominately from one direction, turn the plant regularly. If the seedling turns out leggy, don't throw it away, but when potting on plant it deeper to overcome the problem.
Video advice and tips on successful germination from seed.