What is the proper way to change the DNS IP?

If you have typical connection setup with the network manager and DHCP, try the following:

1. Right click on the network manager icon in the panel and choose "Edit connections..."
2. Select your connection from the wired or wireless tab, choose "Edit"
3. (Enter your password if the connection is set as "system-wide available")
4. Choose IPv4 settings tab
5. Switch method to "Automatic (DHCP) addresses only"
6. Enter the name server you want in the box "Additional DNS servers" and press "Apply"

That should do the trick.

The best way to set a nameserver via the CLI, without NetworkManger, with a static address, or independent of the connection is this:

Install the resolvconf package.

Run

sudo nano /etc/resolvconf/resolv.conf.d/head

(ignore the scary warning. /etc/resolv.conf is autogenerated, so the warning is there so it will get put in /etc/resolv.conf when /etc/resolv.conf is generated.) To the end of the file, add

 nameserver <ip_of_nameserver>

Press Ctrl x and answer yes to saving the file. To finish up, regenerate /etc/resolv.conf so the changes are applied right now:

 sudo resolvconf -u

You can change them like this.

First, click the network manager icon in your menubar, and the click the Edit Connections... item.

Now, switch to the "Wired" or "Wireless" tabs, depending on what you use - I use WiFi, so I'll be using that.

Select the name of your network, and click Edit...

Switch to the IPv4 tab, and then change it from automatic DHCP to Automatic (DHCP) addresses only.

Enter in your DNS server IP address.

Click save, and you're done!