As developers who are comfortable with HTML we normally remove the 'powered by shopify' text in the code behind. But you can also do this by editing the Language settings of your theme:
- In Shopify Admin go to Online Store, Themes.
- Find the theme you want to edit, then click Actions and select Edit Language.
- In the Filter translations box enter 'powered', then press enter.
- You will now see the Powered by shopify textbox. Put a single space in this box.
- Click the save button.