First of all, please note that you won't necessarily have to change your DNS Servers settings. It depends on several factors, among which restrictions set up by your ISP (Internet Service Provider).
How will you know if you have to?
Very simple: if the VPN connection has been successfully established but you can't visit any webpage, you most probably have a DNS issue.
Editing you DNS Servers is very easy
- Go to to System Preferences > Network
- Unlock the padlock in the bottom-left corner if needed
- Select the connection you want to edit (Ethernet, Wi-Fi) then click on “Advanced” (bottom-right)
- In the DNS tab use the “-” and “+” buttons to replace your DNS Servers by 220.127.116.11 and 18.104.22.168 (free OpenDNS service), click OK and then Apply.
- If you are using both Ethernet and Wi-Fi, make sure you edit both.
- You're done!
OpenDNS is the preferred choice: it's fast, secure, does not filter nor log your DNS queries –as opposed to GoogleDNS…