From your Shopify admin, go to Online Store > Themes.
Find the theme that you want to edit and click Customize.
In the left-hand toolbar, click Theme settings.
Click Typography ( in version tf-3.2 or older, the group name is Google fonts ).
For version tf-3.3 or newer
Use font pickers to change the Primary and secondary fonts.
For version tf-3.2 or older
Go to https://fonts.google.com, click the font you want to use. Recommend only select at most 2 fonts for optimizing the loading time.
In each font, select styles you want to use. Recommend Regular(300 or 400), and Semi-bold(600).
Then click the icon on the top right to open the right panel. And click "Embed" in the right panel to open the embed configuration.
Copy the value in the href attribute, then paste it into the URL setting in the theme editor on your store.
Depend on which font you want to use as General or Secondary font, copy the font declaration and paste it into the General Font Declaration setting or Secondary Font Declaration setting. Note: not copy the "font-family:" word.