Make sure you are connected to the network before attempting these instructions.
To add a computer to a domain you need to have that domain's admin username and password or your username should be a member of the domain admin group. (local admin will not work).
Your domain should be setup for DNS server and DHCP server to issue these values when a client computer attempts to connect it.
Before you attempt to connect to the Domain Server's Active Directory, go to the connected network adapter's IP settings and set "Obtain an IP address automatically" and "Obtain DNS server address automatically".
Right click on Computer icon either on desktop or inside start menu, and in the system properties, click on Advanced System Settings.
Go to the first tab (Computer name) and click on Network ID button. This will start a wizard, which will guide you through various steps involved in joining to an existing domain.
You can also use the Change button and enter the Domain name in the member of Domain field and click enter. This will ask you for the domain admin's username and password. Enter them and after authentication the computer will join the Domain and you will get a dialog box saying "Welcome to Domain (Domain name)". If the system could not find the domain's active directory then an error message will pops up. You need to fix the error and try again.