There are two main types of Stargates. An always-on Stargate, and a normal Stargate. For an always-on Stargate, all you need to do is to enter the Stargate. For a normal Stargate, you first need to click the sign of the Stargate to choose the destination stargate before clicking the Stargate's button/coral/chest to open it. Once open, you may enter the Stargate to teleport.
The name of a Stargate is denoted with dashes (-) on both sides. A Stargate's destination is denoted by >NAME<, where NAME is the name of the destination Stargate. The name in square parentheses ([]) is either the name of the network the Stargate belongs to, or the name of the destination server, if the Stargate teleports from one server to another. For a Stargate with no special options, each Stargate in its network connect to each other, meaning that you can teleport from any location in the network, to any location in the network.