How to install plugins
You want to install a plugin or need to update a plugin...how does this work? We will cover all aspects here.
What do I need?
Before doing anything with files, look into everything you need to use the plugin. Do I need to install some other plugins that the plugin I want requires? What server software version am I using, and does the plugin I want support it?
Downloading what I need
Then you go and download every single file you need to use the plugin. Make sure to download a version of the plugin that is compatible with your server software and to download all dependencies of this plugin in the same way.
If you can't find a compatible version in the official builds, see if there are development builds available which you can download instead. Note that these builds are still under development and might have some issues that still need to be solved. In general, if you see builds listed from some time ago, you can know these builds are old and tested enough to be considered safe. Be very careful with very recent builds or builds that were made shortly after another. They could be having some issues that still need to be fixed/found out.
For downloading development builds, you go to a 'Continuous integration' build server. This is a server that automatically builds the plugin. Over there you can see a lot of different builds plus the latest successful build. If the latest build appears to be faulty in the end, be sure to write an issue ticket and state the build # you used.
Development builds, if available, are usually linked at the bottom of the plugin main page together with a warning message.
Installing what I just downloaded
Now you have all the required plugin jar files downloaded and want to install them. First of all, make sure you actually have the server installed somewhere...otherwise there is no place to install the plugin. Be sure to stop the server right now, we can not install plugins while the server is running.
Now, inspect your downloads. If they are archives such as .ZIP or .RAR be sure to extract the files contained first. You can use WinRar, WinZip, 7zip or another kind of extraction software. Some operating systems allow you to open it as if it is a folder as well, not requiring such programs. Collect all 'actual' plugin files. Be sure NOT to open .JAR files this way, they are not meant to be extracted. If you see a 'plugin.yml' then you are doing it wrong.
Now find the 'plugins' folder found in the server root folder and open it. It is here that you place all .JAR files. If some of your downloaded files include a folder, place it in there as well. They contain the plugin's configuration files. Sometimes plugins don't generate these themselves, so then installing this folder is required. If you already have this folder in the plugins folder, there is no need to replace it. (unless the plugin goes cranky over it)
Final step is starting the server and inspecting the server log to see if all is well. If you see anything pop up there, see this page for more help. If all went well, join the server and use /plugins to see if your newly added plugin loaded up properly. If it's red or doesn't show up, something went wrong.