I'm glad I knew to quickly apply a tourniquet, and I'd like to thank my Songbird for her support; I doubt I'd be doing well right now without her.
Edit, 12 hours later: I can type a little better today (still minus a finger and on painkillers), so here's what happened: Hold your hands out in front of you, palms down, about shoulder-width apart. Pretend you have a knife in your right hand, and a scrubby brush in your left hand, and that your hands are over a sink. You've finished cleaning the knife, so you put the scrubby brush behind the sink. You go to put the knife away in the rack to your left, but you miss, and the tip of the knife strikes the back of your thumb, right at the joint.
Lots of blood spurts out of the stab wound, because you hit an artery. You cry out, your fiancée comes over, and she quickly helps you apply a tourniquet to stop the bleeding while you wash it under cold water. The stab wound is small but deep, but doesn't hit the bone, thankfully. But the loss of blood is making you woozy, so you lay down. She applies antibiotics to the cut, and then a bandage, and makes you take a bunch of painkillers, and you spend the next few hours laying down and drinking liquids, trying not to pass out. Eventually, you slowly recover, but your thumb hurts like hell. It's a very small but very deep cut, so there's not much a hospital could do, so you don't go, but it still hurts.
Funny thing is, I know knife safety. I carry a swiss army knife in my pocket, and have since I was 16, and I use it all the time. I've never gotten even so much as a tiny cut from it; I get more injuries from paper cuts than I do from knives. But... all it takes is one mistake.
On the plus side, I learned firsthand that our new steak knives are really nice and sharp! :D