This is the type of seed starting system I use, where each tray can hold 12 6-packs or a total of 72 plants.
Following is my description of how I start seeds, posted several years ago on Facebook. This year, there will be several changes though.
First, I ordered onion plants rather than starting my own seeds. This is because I really should start seeds in December to have decent-sized seedlings to transplant in March. This year, I did not get my manure together with regards to my planning until mid-January.
Second, reading Carol Deppe's newest book (review coming shortly), she made the point that coddling seeds with sterile soil is basically selecting for plants that can't stand a few stray bacteria. So I'm going to skip baking the manure, which was never pleasant anyways; it's VERY difficult to talk me into something I didn't want to do anyways. ;)
(Aside, one day hubby came home and looked at a tray of manure cooling on the counter and in a smart-ass manner, asked me if that was dinner. I replied that if he couldn't tell the difference between that and the meatloaf in the oven, my cooking chores would be a LOT easier in the future).
On to my seed-starting system...Guess what's currently in my oven? No matter what you guess, betcha guessed wrong...
Composted manure!
It's time to start seeds, and seeds germinate best when kept wet. Unfortunately, fungus also grows really well when wet, and there's a fungal disease called "damping off" that can kill seedlings.
In the garden, one wants lots of good life, worms and fungus and soil bacteria. But in seedling trays, the only life one wants is the seed. In the "real" world, each plant produces hundreds of seeds, most of which don't germinate (which is why they produce hundreds). In the seedling tray, the gardener wants most of them to germinate, so has to provide ideal conditions. This is why many places sell "soilless" mix, which is theoretically sterile.
Yesterday, I rinsed all my trays and cells in a dilute bleach solution, also to kill off any potential fungi. Today, I am baking a 9x13 pan full of compost at 200 degrees for 1 1/2 hours. Doesn't smell as yummy as most things, but not too bad.
I have my own way of doing things that has wound up working very well for me over the years.
I start seeds in the size cell that fits 72 to a tray, however, they're in six-packs, which I find much more convenient than actual 72-cell trays. The six-packs are firm enough to carry, and I can plant the entire tray to one type of seed and move it as needed. There's few things I need 72 of, so the giant trays are not as handy at all.
I also strongly prefer square cells to round ones. Just... my experience is that it's easier to get the seedlings out without harming them, with the maximum amount of roots connected.
I fill each six-pack with a mixture - 1 part compost, 2 parts peat moss or coconut coir. I add a tablespoon of lime per quart because peat moss is a bit acidic. They are filled when dry, using a "funnel" made of paper and duct tape.
Then I put 12 of the 6-packs in a tray filled with water to allow them to soak up water from the bottom. By the time they soak water up, the volume shrinks and there's space available on the top. I refill the cells with vermiculite. Then I plant seeds in the vermiculite layer.
Vermiculite is the perfect stuff for germination because it absorbs the heck out of water. Seeds need to stay wet until they absorb enough water to swell and break the seed coat, then grow. But because it's light and fluffy, air can get in to the new roots too, so they don't drown.
After planting each cell with 2-3 seeds, I cover it with a dome so it stays nice and damp inside, and put it on a seedling mat (for heat).
When the seeds sprout, I use manicure scissors to cut the lesser seedlings. If you pull them out directly, their roots may be mixed with the one you're not trying to remove. So I trim them down to one seedling per cell, remove the dome and stick them under grow lights.
Then as the seedlings grow, their roots move down into the layer with compost/peat or coconut coir. The compost is there to feed the new plant. The peat/coconut coir is there to lighten the soil mix, so the baby seedlings can easily move their roots through and so air still gets through. I keep watering from the bottom so the little seedlings don't get washed away by impatient watering.
The ordinary thing is to start seeds in flats, then prick the tiny seedlings out and transplant into the pots. I am way too hamfisted to accomplish this, thus my system which provides both the best way to start seeds in the top layer plus the best way for them to continue growing in the bottom, until big enough to transplant into the garden.
I am starting onions and leeks this week, and these will stay in the cells until transplanted to the garden. Other plants, like tomatoes, get transplanted into larger pots. I have lots of little pots for this, all square again. I also like and often use cowpots for transplanting into.
I'm not sure there's a real advantage to cowpots, though they actually allow the roots to grow through unlike peat pots. However, I like them and also likely just enjoy futzing with my tomatoes as much as possible. But I could futz into regular plastic pots if cowpots became unavailable and do just fine. Also, cowpots are expensive and I argue with myself about them every year.
I've not started onions from seed before, usually do sets. But I have a big enough light tray now to actually grow a reasonable amount of onions from seeds. This week, I will start a total of 12 Giant Musselburgh and Bleu de Solaise leeks, 60 Walla Walla onions (for fresh eating), 72 Southport Red Globe and 108 Australian Brown onions (also for storage). All that food starts in about 3 1/2 trays!
Image credit: Adapted from Wikibooks planting seed starter by Theornamentalist (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons, via Wikimedia Commons.