There are a few ways to join a Rust Server, the first of which is to join using the admin console.
1. Press F1 in-game to open up the console
2. Type the following into the console, replace <your IP here> with your servers IP address:
client.connect <your IP here>
If client.connect does not work for you, try using net.connect.
3. Press enter, and the game will connect you to the server.
The second way to join your rust server is to search for your server in the list. To do this, type your servers name into the search box then wait for the server to pop up.
Once you join your server the first time, you can easily reconnect by clicking on the history tab.
