You can get a lot of guidance from FileMaker's built in online help, which you really should explore a bit before you post basic questions. And if you're really getting in to FileMaker, there are lots of great books too.
Anyway, the easiest way is to use the built-in auto enter feature. Have a field that records modification...
Simply define a text field in Manage Database>Fields - maybe called <d_ModifiedBy_ae>.
Once it has been committed, when selected, the <options> button is available.
Select <Auto Enter>. Check the Modification box and select Account name from the dropdown to its right...
Click OK and you're done.
Chris's solution will record whoever last edited the full record (any field), which may be all you need.
However, if you want to know who edited a specific field -- we'll call it "myField" -- you will need to use Auto-Enter by Calculation, something like this:
- Evaluate ( Quote ( Get ( AccountName ) ) ; [ myField ] )
Check my syntax in the calc engine to be sure the above is cleanly written; I'm working from memory here.
You may also want to put conditions (Case statement) inside the QUOTE section for when to change it depending on what is entered, or even to have the tracking field rocord both what was changed and by who and when with a running log. These techniques are available, if needed, in many of the 3rd party manuals.