Why does nobody advise the easiest method: simply upload the zip-file (well, the right one of course, with only the plugin files in the zip-archive), WordPress will check whether it already exists, let you know which version is installed and which version you just uploaded, and ask you if you want to replace the old version with the new one. As simple as that.
This was introduced a few WordPress versions ago, I forgot which version exactly.
And this not only works for plug-ins but for themes as well.