How do I install Pi-hole on a Synology NAS?

Ah I assumed you have nano installed, my mistake, is your DSM bootstrapped with ipkg ?
If not:

vi /usr/local/etc/rc.d/S99pihole.sh

copy/paste the data, now:

press: escape
press: : 
enter: wq!
press: enter

Sorry vi is complicated if you have never used it before.