So first off, a lot of this is dependent on how you indexed the field - analyzed or not, what kind of tokenizer, was it lowercased, etc.
To answer your specific question concerning regexp queries, assuming your field is indexed as "smith" (all lower case) you should change your search string to "smit.*" which should match "smith". "smit." should also work.
The reason is that in regexp (which is different than wildcard) "." matches any character. "*" matches any number of the previous character. So your search would match "smitt" or "smittt". The construct ".*" means match any number (including 0) of the previous character - which is "." which matches any. The combination of the two is the regexp equivalent of the wildcard "*".
That said, I'd caution that regexp and wildcard searches can have significant performance challenges in text indexes, depending upon the nature of the field, how it's indexed and the number of documents. These kinds of searches can be very useful but more than one person has built wildcard or regexp searches tested on small data sets only to be disappointed by the production performance. Use with caution.
http://www.elasticsearch.org/guide/en/elasticsearch/reference/current/query-dsl-regexp-query.html
ElasticSearch Regexp Filter