Hello folks!
I'm have trouble with my DHCP server on my linux box. I would like for it to assign the DNS dynamically because I won't know if the DNS that I'm using might change one day.

eth0 = internet connection cable, IP changes once every 3 months (if that matters)
eth1 = 192.168.66.1 to the LAN

i'm just lost in what I should have in my dhcpd.conf file. What can I add for it to assign to clients the DNS dynamically?

I would do it slightly differently. You can easily install a DNS server on the system that runs DHCP, point the clients at that, and set your DNS server to use your ISP's DNS server as a "forwarder". That way you can have a fully functional private network and a change to the ISP's DNS server means altering just one text file.

Check out dnsmasq, which is a great piece of software specifically designed for small networks that will handle both DHCP and DNS (dynamic). I'd only recommend using BIND and dhcpd over dnsmasq on a home network if you are doing this to teach yourself, or have more complex requirements.