I should have done this a bit differently, but I didn't. I put the dirt right into the tank, got it a little wet (about the consistency of a lumpy SnakPak pudding) and mushed it around. Kinda fun playing in the mud. Anyways, I thought I would will the tank half full of water at this point so I could scoop out all the little wood chunks and other crap i could see that would float.
The mud stayed on the bottom for the most part, but I'm sure a lot of nutrients were pulled out and into the water. I should have "capped" the dirt right after the SnakPak stage and worried about floaters if/as they came through. (I'll explain "capping" soon. Just for the noobs like me.)
Here's just some of the crap I netted off the top. LOADS of stuff came up.