Your post already uses the key term for one of two ways that you can set up an "OR" type set of search criteria: Request.
When you enter find mode--either manually or via a script, You get one blank "request" on your screen instead of the record showing data. You then fill this out as a kind of "example record" and when you perform the find, FileMaker finds all records in the layout's table that match that example.
One way to do an find with OR type criteria is to create additional requests and enter different criteria in each request.
Enter find mode and type "Fred" into a text field.
Select "new request" from the Requests menu and enter "James" into the same text field.
Perform the find.
FileMaker will find all records with "Fred" or "James".
In a script, new record/request creates a new request if a preceding script step has entered find mode.
The second method is to perform a find for "Fred", then return to find mode and specify "James". But instead of clicking Perform find in the status tool bar, you select "extend found set" in the Requests menu. This will find all "James" records and add them to the found set of "Fred" records.
Here's a thread on scripted finds that you may find helpful: Scripted Find Examples