To configure a static IP (an IP that will never change) in debian you must edit the file /etc/networking/interfaces and do the following changes.
Determine the interface you want to make static. (If there are multiple)
The edit /etc/network/interfaces and find the following line.
iface eth0 inet dhcp
Replace it with this:
iface eth0 inet static address 192.168.1.10 netmask 255.255.255.0 network 192.168.1.0 broadcast 192.168.1.255 gateway 192.168.1.1
Make sure you replace all values so they fit your network settings.
Restart the network interface to enable the changes. After running this command you might get logged out when then network interface is down.
$ ifdown eth0 && ifup eth0
Check if all settings are correct.