We are going to install the plug-in by extracting the CostcoExport.lrdevplugin folder (and its content) contained in the zipped package. Depending on your operating system, the target path for the installation is as follows:
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Since I am running Windows Vista, I am going to install the files to %USERPROFILE%\AppData\Roaming\Adobe\Lightroom\Modules. The screenshots below illustrate the installation process.
After extracting the files, your installation folder should look like this: 
Now that files have been extracted, we are going to launch Lightroom and activate the plug-in.
Activation
You can go directly to the Lightroom Plug-In Manager by choosing File | Plug-in Manager... from the main menu or by pressing the arcane key combination Ctrl+Alt+Shift+. Costco Photo Center should appear in the list of installed plug-ins on the left hand side - click it so the Plug-in Manager displays the plug-in details in its main panel on the right hand side:
Click the Activate Plug-in... button, the Plug-in Activation window comes up.
Enter your first name, last name, and the serial number exactly as they appear in the registration e-mail from alloyphoto@alloyphoto.com. Then click Activate...
Once your information is validated, Lightroom will display a confirmation message:
Now you can click Done to close the Plug-in Manager and start uploading your pictures.