If you are not a developer then "upgrading" isn't relevant to you in most cases.
If you have software running on .NET Framework 4.x then you can upgrade the OS to .NET Framework 4.8.1 and those apps will use the newer version. There can be only 1 version of .NET Framework 4 on a machine and all apps that rely on it use the same version. This is the only "upgrade" you can really do.
If you have software running on .NET Core 2+ then you can install a newer version (only .NET 6 and .NET 8 are supported and .NET 6 is going out of support later this year). However that is meaningless for the most part because software built against NET Core must run on the major version (e.g. 2.x, 3.x, 5, 6, 7 or 8) they were compiled against. The only way you can "upgrade" that software is by having the developers/publisher upgrade their code first. You can then install the version of NET Core/6/8 that they need on the server. Installing it without upgrading the software does nothing as it won't be used.
Also be aware that it is possible to build software against NET Core/6/8 apps that are self contained. In this case they ship with the framework components they need and won't use whatever you have installed on the machine at all. Same situation here, the developers have to update the runtime themselves and ship a new version. You don't have to install anything on the server in that case.
As for whether it requires a reboot or downtime - in general no. Installing a newer major version doesn't impact anything because nothing can run against it yet. Upgrading an existing version to a newer patch won't generally require a reboot as running software will just continue to use the older version until they restart.
An exception exists for web apps. If you are running IIS and the app(s) you're running need NET Core/6/8 and you are installing a major version then IIS has to be updated to support the newer version. In order for that to take effect IIS has to restart. That means that any existing web apps (irrelevant of whether they are using NET Core/6/8 or not) will be temporarily down. IIS generally restarts in seconds so it is blip in most cases but you should plan accordingly.
As for the runtime to install you should go to the NET Downloads page. There are 3 runtime downloads available. If you are running web apps then use the web hosting bundle. This takes care of installing the core components, web pieces and updating IIS. If you only run desktop/console apps then you can just install the desktop bundle. This excludes the web/IIS components (since they aren't installed).