You can see the first loom project I made here. I might make a slouchy one with the earth tones yarn, too. Because, well. Winter is cold here.
Pattern: e-knit 1 row, knit 24 rows, pull up loops for brim and knit off, e-knit 27 rows, transfer every other peg's loop to the peg next to it, knit off, sew through remaining loops and cinch together, tie off on the inside.
After finding a pile of loom knitting hat patterns on the internet, I got the gist of what's involved, and then just got going on this hat. If you only e-knit the whole hat, a large circular loom makes a regular hat, and an extra large circular loom makes a slouchy hat with a very roomy brim. Regular knit stitches are a lot tighter, and will snug up the brim more on an extra large circular loom. Be prepared to have a sore dominant thumb, though.
I tore a ligament in my dominant thumb a couple of years ago and making the brim with knit stitches definitely aggravated it, so I can't use this method often (pretty sure my thumb is arthritic already, but I don't want to make it worse if I don't have to). Good thing this brim worked on the first try.
Have you tried loom knitting? It's fairly fool-proof. Give it a try. What have you got to lose? :)