If you purchased your theme directly from Shopify, it will be automatically installed when you log into your Shopify admin.
If you purchased your theme from pixelunion.net, you'll receive your theme as a .zip file named something like
Upload your new theme
Once you've downloaded the theme file, go to your Shopify admin dashboard and navigate to Online Store > Themes. Then click Upload theme. Select your theme file from your computer and click Upload. Your new theme will show up below your current theme.
At this point, it is installed, but not published. When you're ready to unveil your new look to the world, click Publish theme.