The match query supports fuzzy matching out of the box:

GET /my_index/my_type/_search
{
  "query": {
    "match": {
      "text": {
        "query":     "SURPRIZE ME!",
        "fuzziness": "AUTO",
        "operator":  "and"
      }
    }
  }
}

The query string is first analyzed, to produce the terms [surprize, me], and then each term is fuzzified using the specified fuzziness.

Similarly, the multi_match query also supports fuzziness, but only when executing with type best_fields or most_fields:

GET /my_index/my_type/_search
{
  "query": {
    "multi_match": {
      "fields":  [ "text", "title" ],
      "query":     "SURPRIZE ME!",
      "fuzziness": "AUTO"
    }
  }
}

Both the match and multi_match queries also support the prefix_length and max_expansions parameters.

Fuzziness works only with the basic match and multi_match queries. It doesn’t work with phrase matching, common terms, or cross_fields matches.