Where/how you can install it greatly depends on the platform. If your webserver is a *nix flavour of some sort you should be able to install Node on it.
If you have a managed hosting account on a shared server, you might need to simply send an email to the hosting provider, many will be happy to help out with custom software requirements.
As for installing it at home, if you have Windows it's a bit harder, but not impossible (installing node on windows - Google Search).
The method you're using to store/generate/manage your content, should be one that you're comfortable working with. Whether that be (Node) JS, PHP, Ruby, etc.
Personally, PHP has generally been my preferred platform on the server; though, (slowly,) I too am beginning to experiment with Node