Linux: extract the SH file to your home directory and execute it via a terminal console window.
This will move script files into your Autodesk plugin path. The exporter should then be available in the Custom shelf in Maya.
Models are exported in FBX format. The FBX plug-in comes with Maya and should be automatically installed and loaded. If it's not, you can find instructions for installing it in the Autodesk Knowledge Base. You can check that the plug-in is loaded from Window → Settings/Preferences → Plug-in Manager. It will be in the list as fbxmaya.bundle (Mac OS X) or fbxmaya.mll (Windows).
In order to preserve texture information, it's important to check your FBX export settings. Go to File → Export All... and choose FBX export from the Files of type drop-down. In the options, make sure Embed Media is enabled. Under FBX File Format, you can also change Type to Binary, which will reduce file sizes and upload times.
How to use
Click the script icon to open the Sketchfab Uploader window.
If this is your first time running the exporter, go to Settings → Sketchfab Settings, enter your API token and any default tags (stored for future use), then Save.
Enter a title, description, tags, and mark it as
Draft if necessary.
Click Upload to Sketchfab!
If successful, the model's URL will appear.
When the upload is complete, you can view your model on Sketchfab, adjust rendering settings, and save the default view. Any errors and warnings, such as issues with texture formats, will be logged in the Script Editor (Window → General Editors → Script Editor), as well as a log file in your Maya preferences directory.