An Employer Identification Number (EIN) is the nine-digit federal tax ID the IRS assigns to businesses and other entities, written in the format XX-XXXXXXX (IRS Publication 1635). Despite the name, it isn't only for employers: the IRS says you generally need one to hire employees or to operate a partnership or corporation, among other cases. It costs nothing: in the IRS's words, “You never have to pay a fee for an EIN.” If you show it on an invoice, it goes in the seller block under your business name, labelled “EIN”. A client that must file an information return about payments to you will ask for your number on Form W-9, which exists “to provide your correct Taxpayer Identification Number (TIN) to the person who is required to file an information return with the IRS”. Example: “Example Studio LLC, EIN 12-3456789” (a placeholder). Common mistakes: paying a third-party website to get an EIN, and, if you use your Social Security number as your tax ID, printing it on invoices instead of giving it only on the W-9.
Try it: Invoicing in the US.