The most general way is by date. All quarters dated 1964 and earlier are made of 90% silver alloy, and all circulating quarters dated 1965 and later are made of copper-nickel clad composition (NOT nickel plating; there's a major difference).
The US has struck quarters in silver since 1965, but all of these carry an S mint mark and were made for inclusion in special collectors' sets. Specifically, some 1776-1976 Bicentennial quarters were made of a 40% silver clad composition, and since 1992 90% silver composition has been used in special "Prestige" proof coins.