Adding a button to run a macro is easy enough, but the biggest obstacle that you have to overcome is that in order for this to work, the user must allow the macros necessary to achieve it to run, and you cannot force that.
If the form is not created on a web site to be filled on line, I would be inclined to send out the form as an e-mailed attachment and include an instruction to return the form to you as an attachment. You can include a hyperlink - and it might be better not to encourage the user to change the subject as it makes it much easier to identify the returned messages for processing, if they all have the same subject, to which end you should find
http://www.gmayor.com/ExtractDataFromForms.htm useful.