The following explanation is based on information taken from the site Englishpage.com:
Have someone do something
This construction means "to give someone the responsibility to do something."
1. I will have him help me.
Get someone to do something
This construction usually means "to convince to do something" or "to trick someone into doing something."
2. I will get him to help me.
Sometimes "get someone to do something" is interchangeable with "have someone do something," but these expressions do not mean exactly the same thing. Examples are here