remove everything before the last occurrence of a character

You have the right idea just replace the brackets with parentheses.

var string = "/Roland/index.php";
var result = string.substring(string.lastIndexOf("/") + 1);

Here is an example in jsfiddle and here is an explanation of the .lastIndexOf() method on the Mozilla Developer Network.

Personally I'd use a regular expression:

var result = string.replace(/^.*\/(.*)$/, "$1");

If you're familiar with regular expressions (and you should be if not :-) then it's not as alien-looking as it is when they're unfamiliar.

The leading ^ forces this regular expression to "anchor" the match at the start of the string. The \/ matches a single / character (the \ is to keep the / from confusing the regular expression parser). Then (.*)$ matches everything else from the / to the end of the string. The initial .* will swallow up as much as it can, including / characters before the last one. The replacement text, "$1", is a special form that means "the contents of the first matched group". This regex has a group, formed by the parentheses around the last .* (in (.*)$). That's going to be all the stuff after the last /, so the overall result is that the whole string is replaced by just that stuff. (If the pattern doesn't match because there aren't any / characters, nothing will happen.)

Split the string into an array on / and .pop() off the last element. Note, that you will first need to strip off a trailing slash if there is one.

var locationstring = window.location.pathname;
// replace() the trailing / with nothing, split on the remaining /, and pop off the last one
console.log(locationstring.replace(/\/$/, "").split('/').pop());

If in the case of a URL like /path/stuff/here/ where you have the trailing /, if that case should return an empty string rather than here, modify the above to remove the .replace() from the call chain. I assumed you would want the last component regardless of a trailing slash, but may have incorrectly assumed.

console.log(locationstring.split('/').pop());