The short answer
Get them medical care first, then write down exactly what happened while it is fresh, then call your insurance agent the same day. Do not admit fault and do not offer cash to make it go away, and never ask an injured worker to sign anything at the site.
The first hour
Care comes before paperwork. Call 911 for anything serious, and drive them to urgent care for anything that is not.
Never talk someone out of going. An employer who discourages treatment turns an insurance claim into a much worse kind of problem.
Stop the work if the hazard is still there, and make the area safe before anybody else walks into it.
Write it down while it is fresh
Within the hour, write out what happened, when, where, who saw it, and what was being done at the time. Take photos of the area and of any equipment involved.
Get names and phone numbers for every witness before people leave. On a day labor job, the crew scatters at the end and nobody is findable next week.
Call your agent the same day
Report it even if it looks minor and even if you are not sure it is covered. Almost every policy requires prompt notice, and late notice is a reason insurers use to deny a claim.
Let the insurer decide coverage. That is their job. Your job is to report it and to tell the truth about what happened.
What not to do
Do not say it was your fault, and do not say it was theirs. Say what happened and let the adjusters sort out the rest.
Do not hand somebody cash at the site to settle it, and do not ask them to sign a release there. It looks like exactly what it looks like, and it can void your own coverage for failing to report.
Do not fire somebody for being hurt or for reporting it. Retaliation is illegal in every state and it turns a covered injury into a separate lawsuit.
Who ends up on the hook
If the person was your employee and you carried workers compensation, that policy handles it, and it usually ends your exposure to being sued.
If they were your employee and you had no coverage in a state that required it, the medical bills and lost wages can land on you personally, along with a state penalty.
If they were a true independent contractor, their own insurance or their own health coverage is generally first in line, and you may still be exposed if the injury came from a hazard on your property you knew about.
After the claim
Keep every document in one place. The report you wrote, the photos, the medical paperwork you receive, and every email from the insurer.
Then fix the thing that caused it. The most expensive version of this story is the one where the same hazard hurts a second person after you already knew about it.
This guide is general information, not legal, tax, or insurance advice. Rules differ by state and by situation, so talk to your own professional before you rely on it.