The checkout page can be translated as long as you are using the new responsive checkout.
It works just like the translation of your own content, check the Knowledge base for detailed information on how to translate you page or follow this short overview:
Translating the checkout page
Navigate to the "Translations / Theme Translations" section in langify and choose your main theme.
Unfortunately the product name and custom payment/shipping info cannot be translated on the checkout page and will always show up in your base language.
For The Old Checkout
If you are still using the old checkout instead of the new responsive checkout, you won't be able to translate your checkout page using langify.
You can, however, use a workaround that allows you to display two languages on your checkout page:
shopify allows you to translate your checkout page into any language you want.
Instead of translating into only one language, you simply translate into two languages separated by a delimiter so it looks like:
First Name / Vorname:
shopify has a documentation on how to translate your old checkout page available here:
http://docs.shopify.com/manual/settings/checkout-and-payment/checkout-language
Good luck!
We hope this tutorial was of use, if you are still struggling with your translations or have encountered any problems which we haven't discussed here feel free to contact us.