There are two basic ways:
1. Use mod_rewrite to rewrite /watch to /watch.php
2. Create a file called "watch" and configure your web server to treat it as a php file
Personally I normally use the second, e.g. in .htaccess (Assuming Apache here)
<Files watch>
ForceType application/x-httpd-php
</Files>
Be aware that this will cause any file called "watch" any number of directories deep to be treated as PHP.
In the file "watch" you could easily just do require 'watch.php'. This is helpful as it means you have less PHP code in a file which doesn't end in .php, which could confuse your editor (or developers etc).
Mark