Here's a 5 bullet point methodology for finding XSS.
I don't like XSS but I must look for it as part of the pentests I perform for clients.π
1. Perform source code review
Most pentester and bug hunters don't. And you don't need to be a top coder/developer to do code review.
2. Identify entry points and user-controllable inputs
Also, look for sources and sinks.
3. Perform black box testing with manual input
This works synergistically with #1.
4. Use automated scanning tools to detect potential XSS vulnerabilities.
You might clear out many low-hanging fruits. Mostly in pentesting, very unlikely in bug bounty hunting.
5. Leverage browser tools like DevTools or Burp Suite to identify potential XSS.
Very few professionals use DevTools. Use it to gain a competitive advantage.