from the IRS site: "An Employer Identification Number (EIN) is also known as a Federal Tax Identification Number, and is used to identify a business entity. Generally, businesses need an EIN. You may apply for an EIN in various ways, and now you may apply online. This is a free service offered by the Internal Revenue Service. You must check with your state to make sure you need a state number or charter."
EINs have two digits, a dash, then seven more digits.
There is no freely searchable database of FEINs maintained by the government. If a company has lost or misplaced their number the IRS will look it up and release the information to an authorized person from the company. There are several commercial fee-based services on the web.
If you know the state of the company, try searching the state's database of registered companies to see if the FEIN appears in the company's filing.
For public companies, the EIN or IRS number should appear on the first page of various filings with the Securities & Exchange Commission.
For non-profits, try searching for their form 990 tax filing.
For political organizations, try searching for their form 8871 tax filing.
For insurance companies, try searching for their financial statement filing.
For private companies, try searching their web site if they don't show up in a state agency database. You can also try looking for UCC, court or bankruptcy records, but you'll probably end up needing to use a commercial service.
If you've seen recommendations elsewhere to try searching in LexisNexis or Westlaw, that is referring to the commercial versions which are not available at UCF. The academic subscriptions for LexisNexis and Westlaw do not include files used for conducting public records searches.