Hello Stephen, 

I think the easiest way to achieve this would be to turn tracking on the fields you want to be logged, this will put any changes in the chatter and the user that changed the fields (example).  

You can edit this in Studio, if it is a custom field, by selecting the field->more and the adding a number into the "tracking" field. 

This video may help you more if you are doing this with a custom module. 

I hope this helps,

Thanks,