State "Second Printing" on the copyright page. This is certainly the simplest method, especially for a publisher that hasn't established a code that collectors can recognize. You might want to add the date of the new press run, just to offer a bit of extra information.
Print a sequence of numbers or letters of the alphabet in a row across the copyright page, right from the first printing. For each later printing, delete one character in the row. In the second printing, for instance, the row would begin with the numeral 2. This was an especially useful tactic in the old days of printing in "hot lead," when one indicator character per printing could be literally scraped off the printing plate. Some publishers run the characters straight from left to right; others put the highest number in the middle of the row --- 1 3 5 4 2 --- so that the line of characters stays centered on the page as the printing number goes up.
Give the first printing a distinctive character that you can simply remove from later printings. The most famous use of this method is by Scribner's, who since the 19th century has printed an elaborate capital A on its first-printing copyright pages. It's enigmatic only to those who've never worried about identifying first printings.