So you have a couple hundred seedlings in a tray and it's definitely time to put them into pots.
I found myself in that situation when several hundred seeds that I was "fermenting" in water suddenly sprouted. The fermentation process is used for loosening the jell around seeds fresh out of the mother tomato so that they can be rinsed clean and dried without sticking together and put into envelopes, etc. for safe keeping.
I forgot a portion setting on a shelf. They had been setting in water for several Months before I discovered them. They had been setting since last November 2008, through Christmas and New Years and into the first of April in murky water. There seemed to be some with tiny roots poking out of the floating seeds when I discovered them. Naaaaaaa. They couldn't be viable. They couldn't still be Alive! But, these seeds were valuable to me. These tomatoes [ "Pinks" ] had barely been touched by Late Blight last year, when 14 expensive Hybrids with all the Fancy initials showing Resistance to several diseases succumbed just at the bearing stage. The "Pinks" each bore buckets of nice medium sized tomatoes. These 2 plants were less than 20 feet from the Hybrid patch. Yes. These were valuable seeds.
So i poured the whole mess out into a tea strainer and begin to rinse them under tepid faucet water. Yes. Those were definitely roots! But were they alive. Have you ever tried to plant little wet tomato seeds in blobs a furrow? Even small furrows in a tray with an inch or so of soil. Can't be done.
All I could do was put a little blob of seeds here - and a little blob there. Then scatter a little soil over them. Press gently in and mist them with a little water. And this is where the story starts.
Over 200 baby tomatoes come up topsy turvy - roots entwined - and thick as fleas in my small paper tray. Aunt Jemima Microwave Breakfast trays. I seem to have centered on them as great trays to start or test seeds in. One stacked upon another. The top one is the seed tray with holes in the bottom for drainage and watering, and the second one underneath with no holes uses as a drip tray. Works for Me! But I digress....
First dampen the seed tray so the soil doesn't dry out quickly. Tiny roots will be exposed to the air for short periods of time. They must not dry out.