Once you report the incident to your employer (which should be immediately), they complete paperwork and you should receive some paperwork from the industrial commission (depending on what state). Fill it out and return it, your company should do the same. You get paid (tax free) for as long as you are 100% out of work. I was out 6 months and the industrial commission sends your company paper checks on a weekly basis amount based depending on your salary. Your company should forward them to you on payday. My checks were significantly larger due to the no tax but i still think its close to only 70-80% of your regular salary.
Once your claim is completed, you will receive a lump sum check based on percent of disability reported by examining doctor and the value of what your body part injury is.
Get a lawyer. They are free until you win. I can only speak for my state which isn't NY.