You can download a Parsec installer from the downloads section, for any of the supported operating systems contained there. Make sure to get the correct 32 or 64-bit version for your system to avoid issues while installing. You can also check the articles for the supported hardware for connecting to a computer or hosting your computer.
If your download isn't finishing, the installer file is disappearing, or the installation is ending prematurely, check if your anti-virus is interfering. A common culprit is Segurazo / Santivirus / Segantivirus, it commonly causes installation issues and most of our users don't even know they have it installed. If you have it, uninstall it completely and restart your computer. In newer variants of Segurazo, you will need to use safe mode and use something like Malwarebytes to remove it.