Hi Chris. And welcome to ATP!
Seedlings need no fertilizer until they have at least 1-2 pairs of true leaves. (The initial pair of round leaves, the seedling leaves, don't count.)
Then, give them VERY LITTLE fertilizer, like 1/4 as much as the jar of fertilizer recommends. They don't need or want much. besides, you want them to grow strong roots and a short, sturdy stem - not shoot up on a spindly stem or get leafy at the expense of roots.
So fertilize them weakly, weekly or every few weeks, at first.
Technically, it depends a lot on the "Nitrogen number", the first number in the labels' "24-8-16". Practically, Miracle-Gro all purpose plant food suggests
"For indoor plants, mix 1/2 teaspoon (not tablespoon) per gallon of water. "
In that case, you would use at most 1/8th teaspoon per gallon for seedlings, and don't use it very often, either.
I can't tell where you live, so I don't know if you;re ready to plant out yet.
When you do, remember that FIRST you want the young plants to grow strong roots. Make them work for it! If your soil is at all fertile, don't fertilize for a while, then go gently rather than give them too much.
Hopefully, tomato experts will chime in and give solid numbers for fertilizing adult plants. But if you aren't sure, give them less fertilizer until a few leaves start turning yellow. Then you know you will be fertilizing, not OVER-fertilizing.
What's the downside of under-fertilizing? Maybe, eventually, they will grow somewhat less slowly if your soil is infertile. How to recover? Give them a little fertilizer and the plants will take off.
What's the downside of OVER-fertilizing? Burn the roots, stunt the leaves, stop growth for weeks, maybe never recover, or, quite commonly, kill the plants. How to recover? MAYBE recover part way by flushing the soil, but more likely you'll have to start over with new plants or chalk this year up to "experience".
P.S. I;'m not a totally organic kind of gardener, but they have a great point. "Feed the soil, and the SOIL will feed the plants". Just go back in time a year or two and start feeding your garden soil lots of compost. Then you won't need much fertilizer until your plants are huge and growing fast.
Good luck, and I hope I see you around the forums here at ATP.
