It's my first time hosting a server and I'm not sure how it works with Rust updates and plugins.

My questions is;
how long does it take for plugins to update?
Do I need to do anything?
Do I need to reinstall plugins?

Unless a plugin broke, an update is not necessary for those. Update times depend on whenever the developer of that specific plugin is able to.

When there is a Rust update it is best to STOP the server then update Steam,Oxide and Rust io (if you use it) then START the server,
You will notice on the "plugin" pages of the plugins on this site that there is a "Watch" button, click on it and it will notify you if there is an update to that plugin,
The only recommendation i can make is ensure that you read the "documentation" page of the plugin and info page regarding the update in case you have to back up the data or config files before updating, Nothing is more embarrassing than losing all  your players ranks/rewards/data if you forget to do it,

Nice one fellas.

So it's best to keep the server off until I think there are enough plugins for it to run, then turning it back on the plugins should start normally?

Where will I be notified? Here? Email??

Thanks for the help

Plugins will automatically load themselves whenever the server restarts. 

What I meant was, do I need to update the plugins myself or should the update just go through by itself? 

Yeah, you need to update them yourself. 

How do I go about doing that? 

As @pookins said up there ^^^, every plugin has a "Watch" button on the plugin page.



Click that and you will get notified if there is an update for that particular plugin. If there is an updated version, simply download it then copy it into your servers oxide\plugins folder. It will ask if you want to overwrite the existing file, click yes and it will overwrite. The update notes on the plugin page should let you know if you need to change anything or update the plugin in a particular way.

The server can either be running or switched off when a plugin is installed/updated. Bear in mind though, if the server is running and you install a plugin, the server will load it straight away and the playerbase might get a shock with new stuff popping up on the screen, etc. Best to initially read the ENTIRE documentation that is on the plugin page, make yourself familiar with it's permissions etc then install it, assign the needed permissions then away you go.