Installing a package on a fresh system is remarkably straightforward. Simply download and install the package using whatever utility your distribution provides. There is usually no need to explicitly remove old packages before installing, as modern Linux distributions should upgrade and replace them automatically. If you installed Wine from source code, however, you should remove it before installing a Wine package. See the section on uninstalling Wine from source for proper instructions.
Wine works on a huge amount of different Linux distributions, as well other Unix-like systems such as Solaris and FreeBSD, each with their own specific way of installing and managing packages. Fortunately, however, the same general ideas apply to all of them, and installing Wine should be no more difficult than installing any other software, no matter what distribution you use. Uninstalling Wine packages is simple as well, and in modern Linux distributions is usually done through the same easy interface as package installation.
We won't cover the specifics of installing or uninstalling Wine packages among the various systems' methods of packaging and package management in this guide, however, up to date installation notes for particular distributions can be found at the WineHQ website in the HowTo. If you need further help figuring out how to simply install a Wine package, we suggest consulting your distribution's documentation, support forums, or IRC channels.