I would say that wordpress is actually the easiest platform to hack. Not because wordpress itself is very vulnerable, but because most plugin developers has little to no knowledge about security. XSS, CSRF and SQLi are all over the place.
Like stated by others you should find out what plugins they have installed, this can of course be done manually, but I would suggest you use WPScan for this. It gives you three options on enumerating plugins
1) p - Plugins (looks for around 2k plugins)
2) vp - Vulnerable plugins only
3) ap - All plugins (this looks for an installation of every single plugin on wordpress.org - last I checked it was just over 36k plugins)
The result will give you info if any of the existing plugins are vulnerable. If you don't find anyone with known vulnerabilities you can analyse the code yourself to see if you can find some holes (the beauty of open source) either in the svn repo on wordpress.org or download the plugin.
You could also, as mentioned earlier, look for other installations... One method is to look for this is to search for sub domains. To do this go to google and type the following
Code:
site:domain.com -site:www.domain.com
This will return all indexed results on this domain excluding all starting with www
Hope this helps a bit

Happy hacking