Broken blood feathers are easy to deal with, and every bird owner should know how to handle this. Too many people freak out over them, when it's really quite simple.
First off, read this article. It has pictures:
Blood Feathers
Next, go buy yourself a hemostat with wide jaws. If you don't know what that is, it looks like a pair of scissors, but with gripping jaws instead of blades.
Hemostat - Wikipedia, the free encyclopedia
You can either order one online, or try to find one locally. Try flea markets, gun shows, military surplus stores, hobby shops, or anywhere that sells military surplus, emergency medical, or electronics equipment. I actually bought one at radio shack a few years back - dont think they carry them anymore. DO NOT SCREW AROUND WITH TWEEZERS!!!!!!!!!!!!!!!!! If you can't find a hemostat, use needle nose pliars... but get a hemostat!
If you have to pull a broken blood feather, it will likely either be either a wing primary or tail feather, because they're large, and likely to be damaged while the bird is flying.
1. Don't panic.
2. Have someone else restrain the bird, and find the exact feather. If it's hard to locate, wet the surrounding feathers.
Do the next steps quickly (within about 5 seconds):
3. Support the part of the body with the feather in question. Simple for tails, but a wing will need support.
4. Clamp down on the feather with the hemostat. Get close to the skin, but not close. About 1/2 inch or so is about right. Clamp so the hemostat is as parallel to the shaft as possible. This does 2 things: first, gives the most surface area of the feather shaft in the jaws of the hemostat, and second, allows you to pull with the feather.
5. With a deliberate, swift motion, pull the feather in the direction of growth. Pretend like you're pulling a fairly stiff lever. Don't jerk, twist, pry etc.
Now, inspect the feather shaft. There should be a smooth, soft bulb at the end. If this is the case, good job. Let the bird chill out for a minute and check for any bleeding or damage to other feathers. You're done.
IF the shaft broke, it likely broke where you clamped, so hopefully you should have enough shaft for attempt 2. Do it again, but don't panic (this is why it's important to have a hemostat with wide jaws!!!!) If this didn't work, you need to stop the bleeding. Use corn starch and pressure, and call a vet. However, if done properly, it won't likely come to this.