Below is a vulnerable XSS target. Think of the page as a simple search engine. Try to deface the search engine and embed a fake password login.
9x0 Search Engine
The method of XSS is based on script injection. Commonly you will be using the GET parameter and HTML/JS injection.
Example:
Input "Banana" into a search box. The site will answer with "Here are possible Banana results". Now, if you instead input "<span style="color:red">Banana</span>" it will output "Here are possible Banana results". You can now inject different HTMl/JS code and see what results you get.