How to extract data from an activity log?

Hi there, 

I am trying to get data out of an activity log, for example, I want the name of the person who approves a record (which moves the record into approved state). 

I want to extract the name of this individual in a script so that I can reference them and give them additional access. 

Any help on this would be great. Most of the links on existing articles are broken and lead to the ServiceNow homepage so no links please!

Kind regards, 

G