The first is to generate a Unique ID for each artist in the artist database, for artists Shane Feeney, Michael Richardson and Sarah Fang their IDs will be SF01, MR01 and SF02 respectively.
Why do you need that specific format for an ID value? An auto-entered serial number is much simpler to set up and much safer to use in setting up relationships between tables. I'd never use such a field as a match field in a "main" relationship (Might use it in special purpose relationships only for data search purposes). If I needed such an identifier to meet the needs of the users who may already be using that method, I'd set up a field for it in the Artists table, but use an auto-entered serial number ot link artists to works instead of this field.
Therefore when a user enters the Artist ID
Wouldn't it be simpler and less vulnerable to error if you simply selected the artist's name from a drop down instead of entering such an ID? It's possible to set up a text field where you can use an auto-complete enabled drop down list of artist names with a script that uses the name to find the previously mentioned serial number for that artist and enter it in the match field of the works table. Then any fields from the Artists table that contain the data you want to see on your works layout can be added to that layout to show data from the Artists table.
Here's a demo file of this method:
FileMaker 12 users: https://dl.dropbox.com/u/78737945/SimpleNameLookupDemo.fmp12
Pre FileMaker 12 Users: https://dl.dropbox.com/u/78737945/SimpleNameLookupDemo.fp7
Ps. Are all your works by single artists 100% of the time? If you have any collaborative works or have the slightest chance that you could have such, a join table between artists and works would be a good idea as you would then have a many to many relationship between artists and works.