Your invoice should have the following information, more or less:
Phone Email, etc.
Client Business Name
Client Manager Name (the person you're reporting to)
Purchaser Order Number (if one is provided)
Date of work - Description of Work - Hours - Rate - Daily Total
[Above for each block of work, typically a full or partial day]
Expense Date - Expense description - Expense Amount
Total for Invoice
The line with the Client Manager's Name is where the manager signs off on (approves) the invoice, before it is forwarded to Accounts Payable.
It is a good idea to describe what you've actually done on a particular day: some people put something like 'IT Services' or 'Software Development'. Better is 'Set up Inventory database, created validation tables, make backup, set up script to back up server at 11:00 PM each night'. In short, make it possible for you to provide a narrative of what you've been doing over time, so they can see how you're progressing.