The extension has an automatic updater built in so you don't have to worry too much about keeping RustIO up to date. That means, unless there are breaking API changes in Rust or Oxide, that most updates are applied automatically when starting up your server. If necessary, automatic updates can also be applied while the server is still running by executing oxide.reload RustIO on the console.
Otherwise, if there are breaking API changes, there'll be a new DLL to download from here, which can also be obtained through this direct link. Make sure to watch this resource to receive an email if a DLL update is required.
Most issues can be solved by taking a look at the manual (especially: Troubleshooting). If that doesn't solve your problem, feel free to join the discussion!