Nature knows best!
An easy and effective way to grow tomato seedlings is to plant a slice of fresh tomato in compost and allow the seeds to just sprout naturally.
Choose a tasty tomato, chop a slice and plant covered with multipurpose compost in a pot on the windowsill. I tried this method and was very impressed. Half a cherry tomato produced 40 seedlings!
Tomato seeds do need a little heat to germinate so cover with clingflm and place in the sun or use a propagator.
If you try this method, let us know how you get on!