To install Mappalachia, you simply need download the latest release of Mappalachia.zip, which can be found on the releases page.
Once downloaded, make a new folder anywhere you like, and unzip all the contents to that folder.
Once unzipped, run Mappalachia.exe, which has a yellow 'M' icon.
When you first launch Mappalachia, it is possible that systems such as Windows SmartScreen will warn you of a potential security risk. However, this is simply Windows being cautious because Mappalachia doesn't have very many users, and you will just need to select 'more info' then 'run anyway'.