This is just a big ol' list of keywords to search and learn about. No particular order. Search each of these and learn a bit about it, and try out all of the techniques you can manage.
Remember to focus on understanding the actual technology you're targeting. Security is fundamentally about learning what the computer actually does, so you can identify cases where the intent doesn't match the practical behaviour. Spend the time to understand the behaviours that you're exploiting, rather than just memorising the tricks - my old boss always used to say "we can teach computer people security, we can't teach security people computers", and it's very true.
- Reflected and stored XSS
- HttpOnly / Secure cookie flags
- HTTP security headers
- Content Security Policy