How can I address salary and taxes as a freelance teacher, writer?

I have begun giving private English lessons to a student whose company is going to pay for his lessons.

They have recently sent me an “independent contractor” agreement, and I am looking for some advice.

I have agreed to a rate of $50/hr.

Do I need to charge them a percentage higher so that my taxes are taken care of at the end of the year? I am not familiar with this process. They mentioned that I would need to fill out a 1099 should I earn over a certain amount. I am confused.

What do I do?

Clearly, they need the documentation for their own business and will do not anything under the table….what implications does this have on my taxes, etc, and what should I do?
Thx Flutherers :)