I have been searching on google for this multiple times and always give up. Here is the best thing I've been able to find on the topic: https://www.elastic.co/guide/en/kibana/3.0/queries.html
This is lacking. For example, how do I search for strings that "start with" a string. Or, "end width"? Or how do I use a regex? etc. I don't want these questions directly answered, I just want a link to the documentation that answers these things.
I am using Kibana 4.
You can check here: https://www.elastic.co/guide/en/kibana/current/discover.html#search
And if you check the request that Kibana does you will see that it actually uses Query String Query with analyze_wildcard:true
option when you search something. So you can check documentation for Query String Query for abilities.