I am looking to allow my users to use their own domain name to access my web service.
For example if I have a user with a profile at example.com/users/david how can I allow david to use exampledavid.com to access his profile page.
I don't want the users to see example.com in the address bar, but instead for david to see exampledavid.com.
Your issue can be solved with URL rewrite and HTTP Header manipulation or reverse-proxy.
Additionaly, you must make sure that exampledavid(dot)com is setup with DNS provider to pass all requests to example.com.
DNS Record Sample:
Ref:
https://en.wikipedia.org/wiki/CNAME_record
http://www.akadia.com/services/apache_redirect.html
http://httpd.apache.org/docs/2.2/mod/mod_proxy.html
http://www.iis.net/downloads/microsoft/url-rewrite