When you fill out your onboarding documents for your sponsor job, you will complete a form called I-9. For information about how to fill out this form, see this article from USCIS. The box on I-9 Section 1 asks about immigration status:
If you have your Green Card or visa, you should check box #3.
If you have your EAD, you should check box #4.
Your sponsor may also have you complete the W-4 tax documents during orientation. See this link for additional information on how to fill out tax forms.