Render the document.
The only JSS specific thing you need to know is the Style Sheets registry. It will allow you to get all attached sheets as a CSS string. Rendering of the document depends on the framework you use, here is an example in react.
Once JS is loaded on the client, components initialized and your JSS styles are regenerated, it's a good time to remove server-side generated style tag to avoid side-effects, example in react.
Here is a live demo with react, SSR and React-JSS.