Wash with soap and water and wrap it in gauze. I had a ton of dog food run over my toe on a pallet jack (yes, 2000 pounds) and lost the big toe nail on my right foot. I didn't know I was gonna need steel toed boots for that job.
My big toe nail fell off too.. first it turned black from wearing tight steal toe boots, took a month before it fell off but I had to clip it off slowly, looks like new nail growing back under. right now I feel like having no big toe nail while walking.
You could probably skip dealing with the tender toe-nail as it regrows by just having your big toe amputated. Cauterize the would and you'll be on your merry way without having to worry about waiting for the toe nail to regrow.
Go to the pharmacy, and buy an antibiotic cream. Most popular brand here in Canada is polysporin... put that on it, than put a sterile bandage over it. Change it once a day, or when it's really dirty looking (bloody), for 3-4 days, until it's less tender.. then leave it alone. If you don'T put the cream, or don'T buy special dressing, it will get glued to the wound because of the blood and hurt like hell when you try to remove it. Best thing to do in that case is get the dressing wet. Wash with water and regular soap when you change the dressing. I'm a ER nurse, if that makes you trust my advice more.