You almost had it already. I think your main issue was this part:
int l = ((int)Math.random()*s.length());
Your (int) cast is misplaced. If you read the javadoc of Math.random() you see that it returns a double value "greater than or equal to 0.0 and less than 1.0". Casting values of this range to int (i.e. simply cutting off all decimal places) will always result in 0, which only prints the first character of the string.
The solution is to first multiply it with the string's length and do the cast afterwards:
int l = (int)(Math.random()*s.length());
If you only want to print one random character, you don't need a loop of any sort, so you can delete that from your code.
See this fiddle for a working example. What you still need to do is think about how to get the input string (hint: maybe read it from System.in).
public static void main (String[] args) throws java.lang.Exception
{
String s = "foobar42";
int l = (int)(Math.random()*s.length());
char ch = s.charAt(l);
System.out.println(ch);
}
And to finally show off in class, you could also have a look at the Random class which could replace the above line with something like
int l = new Random().nextInt(s.length());
and see if you can grasp the difference between those two approaches. Although that is completely irrelevant to your assignment and way out of scope.