Download the package you purchased from nukecoder.com/shop_purchases.html and extract the archive to a local folder.
Now open the file lib/constants.php (modules/Digital_Shop/lib/constants.php for nuke users).

Find the following line:
define('DSN_STRING', 'mysql://dbUser:dbPassword@dbHost/dbName');

You will need to replace this with  your  database info

Example
define('DSN_STRING', 'mysql://gotcha:mypass123@localhost/digital_shop_db');


For the rest,  the default vaules should be OK, but take a look to make sure everything fits your needs.
Be sure to set SHOP_DEBUG to false before making your shop available to the public.

Now use your FTP program to upload all shop files(except for the folder "docs") to your site.

The rest of the installation is web based, so once all of your files have uploaded, point your browser to:
http://yoursite.com/installer.php (http://yoursite.com/modules/Digital_Shop/installer.php for nuke users)
to start installation.

The video below shows the shop installation process.  Use the arrow buttons to navigate between steps.