Connecting to your Rust server is quite simple. Though in order to do this, you need to add the server as a favorite server on Steam.
Adding A Favorite
To add a favorite server, at the top of the Steam application, click View, then click into where it says Servers.
The the text box to enter your servers IP address. Paste your servers IP with the port at the end. Then click add this address to favorites.
After you do that, you can launch Rust. Or you can choose to connect to it from the favorites page with the connect button.
In Rust, there is an option to choose favorited servers. Choose that option. Then you should see your server. You can then join it from there.
Updated on: 06 / 16 / 2020