Assuming you are on Linux, check if php-fpm is running by searching through the process list:
ps aux | grep php-fpm
If running over IP (as opposed to over Unix socket) then you can also check for the port:
netstat -an | grep :9000
Or using nmap:
nmap localhost -p 9000
Lastly, I’ve read that you can request the status, but in my experience this has proven unreliable:
/etc/init.d/php5-fpm status