1. Install an XDebug browser extension, such as XDebug helper (Chrome, Firefox).
2. Start listening to XDebug connections in PHPStorm with the phone icon (see image in step 2 here)
3. Switch on the XDebug browser extension
4. In the PHPStorm configuration go to Languges & Frameworks > PHP > Servers
   1. Add a new server with name and host dev.wiki.local.wmftest.net, port 8080 (or whatever you configured; can be checked with vagrant config --get http_port)
   2. Check "Use path mappings"
   3. Below that, in the "Absolute path on the server" column set /vagrant in the row that corresponds to your vagrant directory, and /var/www to the row that corresponds to the srv/docroot subdirectory
5. You are ready to go; set some breakpoints (by clicking on the empty space on the border to the left of your code) and make a request (reload the page or make it send an AJAX request)

For command-line debugging, instead of steps 1 and 3 you can use the xdebug_on command (and then xdebug_off to disable).