You now have two options: using the WordPress plugin uploader or unzipping the plugin yourself:
Using the Plugin Uploader
Sign in to your Wordpress blog.
Note: This cannot be a Wordpress blog hosted on Wordpress.com, because Wordpress.com will not let you install your own plugins
From the left-hand menu, select "Plugins > Add New"
Click "Choose File" and select the GumGum for WordPress plugin
Once the installation is complete, check the Plugins > Installed menu to make sure the plugin is present. If it's present but an "Activate" link shows below the title, then the plugin needs to be Activated. Click "Activate" to do so.
Click Settings > GumGum and follow instructions to configure your GumGum ID.
Manually deploying
Unzip the gumgum-wp.zip file into your wp-content/plugins directory, so that there will be a gumgum-wp/ directory inside plugins/
Once the unzipping is complete, check the Plugins > Installed menu to make sure the plugin is present. If it's present but an "Activate" link shows below the title, then the plugin needs to be Activated. Click "Activate" to do so.