Read a => String -> a means that a can be any type that is an instance of the Read class. For a type to satisfy that requirement, it has to at the very least have an implementation of either of Read's readPrec or readsPrec functions. Many built in types aready supply an implementation, and you can use deriving to generate an implementation for your own custom data types. 
To specify what you want to read the string as, you can type annotate the call directly:
read "1" :: Int
Or give the function enclosing the call to read a signature so the compiler can figure out what you want:
myFunc :: String -> Int
myFunc s = read s
The signature says that the function returns an Int, so the compiler can infer what type to read s as since myFunc returns whatever the call to read evaluated to.