Go to Releases and download the ZIP file from the latest release. The one that looks like obsidian-clipper-x.x.x.zip.
This ZIP file should be extracted in your Obsidian plugins folder. To find your plugins folder, go to Community Plugins inside the Obsidian settings screen. Click the folder icon on the right of Installed Plugins to open the plugins folder.
Extract the contents of the ZIP file there.
There should now be a folder in plugins called 'obsidian-clipper' containing a main.js file, a manifest.json file, and a styles.css file.