Here's the secret to trimming chicken nails. Go slowly and watch for a tell-tale "dot" to begin to appear. That dot is the beginning of the quick. If you continue to trim after you see the dot, you will get a bead of blood that says, "I told you so!"
Chicken nails can fool you into thinking a lot should be trimmed off because they appear quite long. Some chickens have these long nails, and trying to trim too much off, especially too quickly, results in alarming bleeding. And yes, it hurts the chicken. Quite a lot.
Just in case, have some corn starch in a little bowl at the ready to tip the bleeding nail in. It will stop the bleeding.