Our first response is "the same way you would determine a valid or counterfeit Federal Reserve Note". You would examine it to see if it is what you expect. If it looks like there is something fishy or incorrect with it, investigate further.
Furthermore, the Liberty Dollar warehouse receipts use some of the same anti-counterfeiting technologies that federal reserve notes do, plus some they don't. From the Liberty Dollar website: "Some of the many security features designed into each piece of currency include special paper, microprinting of the Preamble of the U.S. Constitution, the Pledge of Allegiance, the First Amendment, and the introduction to the Declaration of Independence in the border, plus an invisible thread containing a DNA code."
In addition, the actual Liberties (Gold, Silver, and Copper) can be tested themselves for content and purity. Some people have even been noted to say when hearing one being dropped on a table "Wow! That's real silver" - that is, the very sound of the liberties is distinctive and different than the base metal coins produced by the U.S. Mint.
We can also supply the exact size and weight measurements for the rounds themselves, and quality images of the front and back faces for you to check against.