It's glad you chose QuickBooks Desktop (QBDT) Enterprise to help run your business, r_mahc. Let me help you find the payroll ID in the program.
Beforehand, do you mean the client company ID? If so, your client can only see that by clicking F2 on the keyboard. Then, look for the Company Intuit ID.
If you mean the service key, you can go to the Employees menu, select My Payroll Service, and click Manage Service Key. I've added a screenshot below for visual reference:

I'm also including a reference here for ideas for managing your payroll tasks: Employees and Payroll Taxes.
Feel free to return here if you have further issues running payroll in QuickBooks. I'll be here to help. Take care always.