Your state will also need additional tax identifiers, depending on what you do. For example, if you sell retail goods, you will need a tax ID number. If you sell alcohol, you may need a different number. When you go to the company, you'll find that you're under a contract with the client on every project. They don't include you on the "W2 payroll" or deduct freelance taxes on your behalf. At the end of the year, the company that hires you reports to the IRS the amount of money they paid you through a "1099". You will receive 1099 from each client you contract with. That's it, and it's straightforward.
