No doubt this is done to death, so no fluff.
Modify the dhcpcd (DHCP client) configuration file:
sudo nano /etc/dhcpcd.conf
If your router is your DNS server, point domain_name_servers to the router’s IP address as shown below. I’ve pointed mine to the Raspberry Pi.

Append values like this, depending on your setup, to /etc/dhcpcd.conf file:

# This will be different if your Pi is connecting via wifi. I'm on ethernet.
interface eth0
# This is the IP address of the Raspberry Pi.
static ip_address=192.168.1.33/24
# IP address of the default gateway. AKA the internal IP address of your router.
static routers=192.168.1.1
# DNS server to use. Normally the IP address of your router. I'm using my Raspberry Pi for DNS.
static domain_name_servers=192.168.1.33

Restart the DHCP client service or restart the Pi altogether:

# New way
sudo systemctl restart dhcpcd
# Old way
sudo service dhcpcd restart
sudo shutdown -r 0

Now see the IP address:

ip addr show eth0 2: eth0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc pfifo_fast state UP group default qlen 1000     link/ether 33:44:55:66:ee:dd brd ff:ff:ff:ff:ff:ff     inet 192.168.1.33/24 brd 192.168.1.255 scope global eth0        valid_lft forever preferred_lft forever