This should not be difficult.
You can just add the field (VenueName) from the Venues table to your layout that's based on the Events table.
No need to create an extra field in the Events table.
If your relationship between Events and Venues is done correctly you can display fields from both tables on the same layout.
Or you could add the Venue name as a merge field on the Events layout.
Downside about that is that you can't enter data in a merge field in find mode.
@Brian - note that 'lookup' has a specific meaning in Filemaker. As you say, you can copy (by a couple of methods; Auto-calc is one, Lookup is another) the venue name to a field in Events. But it will stay 'frozen' unless you force another update. That is referred to as 'by look-up', and may well be something you want, such as in an invoice table that populate prices upon record creation, and then freezes it.
The method DaSaint suggests is not using a 'lookup', but displaying the live Venue name in the Events Table-based layout, and is almost certainly what you want here.
I'm only bothering to be pedantic because 'lookup' is a term used distinctly in FM, and it might cause confusion later.