I want to re-install my MiKTeX distribution on my computer. What would be the most advisable way of doing it? What is the process of uninstalling the previous version safely and installing the new one?
MiKTeX has no own button or menu to uninstall it.
To be sure to uninstall MiKTeX completely just use the "Windows Programs and Features (Add or Remove Programs)" control panel to delete MiKTeX.
Then reboot your computer.
Then download and install the new MiKTeX from the homepage http://www.miktex.org.
Why the reboot?
The reboot is necessary because the architecture of windows. There is a problem with loading dll's. That is only done by starting windows new (reboot). So if you want to unload earlier loaded dll's you have to reboot. If you forget it your computer can show malfunctions or freezes or can run without problems (if the loaded old dll's do not disturb your running programs). It is better to reboot after uninstalling a software on Windows ...