an very often requested issue. I will show this on Debian Jessie
We assume we want to set a static IP Address for eth0
Create new file /etc/systemd/network/eth0.network. Name is not importend, just the prefix network.
# You can also use wildcards. Maybe you want enable dhcp
# an all eth* NICs
# static IP
# 192.168.100.2 netmask 255.255.255.0
Move your previously used /etc/network/interfaces to /etc/network/interfaces.save. The file is no longer needed (for eth0). If some other NICs defined there leave it and just remove all entries regarding to eth0.
root@debdeb:~# mv /etc/network/interfaces /etc/network/interfaces.save
and enable systemd-networkd unit
root@debdeb:~# systemctl enable systemd-networkd.service
Define DNS Server. You can add the DNS Server either in the Network section of the NIC adapter config (see above) or in /etc/systemd/resolved.conf
Create a symlink
root@debdeb:~# mv /etc/resolv.conf /etc/resolv.conf.save root@debdeb:~# ln -sf /run/systemd/resolve/resolv.conf /etc/resolv.conf
and enable systemd resolver
root@debdeb:~# systemctl enable systemd-resolved.service