Peace Silver Dollar Counterfeit/Authentic Comparisons
The 1923 silver dollar on the left is authentic and the Peace Dollar on the right is counterfeit. As you can see, the date, on the counterfeit has letters that are thinner than the authentic example on the right. The details, in general, don't look well struck plus the luster and color of the coin should give you the impression that it doesn't look "right".
It's important to look closely at any silver dollar's "edges", but that I mean, how well are the edges of the letters and numbers struck. Also, make sure they're the correct font for the series and that the date and mint mark match what was actually authorized by the US Mint. Here's a list of the only years and mints that Peace Silver Dollars were minted Peace Dollar Mintages - Values.