Pagination of results can be done by using the from and size parameters. The from parameter defines the offset from the first result you want to fetch. The size parameter allows you to configure the maximum amount of hits to be returned.

Though from and size can be set as request parameters, they can also be set within the search body. from defaults to 0, and size defaults to 10.

GET /_search
{
    "from" : 0, "size" : 10,
    "query" : {
        "term" : { "user" : "kimchy" }
    }
}

Note that from + size can not be more than the index.max_result_window index setting which defaults to 10,000. See the Scroll or Search After API for more efficient ways to do deep scrolling.