Well, you can add ?page={$page_number}
to the URL that you’re requesting.
See, for example, http://demo.wp-api.org/wp-json/wp/v2/posts/?page=2.
It appears to split the posts into pages of 10.
Reference
- WP-API documentation (I found this in the docs for v1 of the API, but per the sample URL above, it works on v2 as well)