In this case the best approach is going to be to overload the method, as Apex doesn't have any concept of optional parameters.
So to illustrate, your class might look like this:
public void myMethod(String input1, String input2) {
System.debug(input1);
System.debug(input2);
}
public void myMethod(String input1) {
myMethod(input1, 'DEFAULT VALUE STRING');
}
You'll notice that both methods have exactly the same name, but the second method takes only 1 parameter, and then calls the original 2 parameter method putting a default value into parameter 2. In this way, you now have the option of calling the 2 parameter method if you need to, but can also call the simpler 1 parameter method with the same name