You will need OpenMRS running either through standalone or developer version.
1)Download/clone Open web app module's code from here - https://github.com/sunbiz/openmrs-module-owa
2)Refer to basic app mentioned here - https://github.com/namratanehete/owabasicapp
3)Create new app based on this basic app.
4)Create html page with textfield and search button to search concept.
5)Use Get operation of Rest call to get patient - Use "/ws/rest/v1/patient?q=<search query>&v=default" rest call where <search query> should be whatever mentioned in search textfield.
6)Display response in html page.
7)Make a github pull request.