Growing tomatoes from seed is dead simple, you don't even need cloth or anything like that to keep them moist. Just sow the seeds into your soil (which you have already done). Keep the soil moist and keep your pots indoors for now (unless you live a really warm area) and in a week to ten days you should see little seedlings popping up.
Allow the plants to grow up until the true leaves have formed then tip your pots upside down to remove the plants, dig a hole that is as deep as the plants and roots are high and pinch off all the leaves on the plants except for the top leaves and bury the entire stem.
Perhaps add some kelp meal into the hole (an organic slow release fertilizer (tomatoes love it)) and then fill with soil.
As far as a time until planting.... depends on how fast your tomatoe plants grow. You will want to harden them off before moving them outside before repotting or planting them in the garden.
FYI: What works best for tomatoes is a Cedar Stake for supporting the plant and old nylons work great for tying the plants to the stakes.