How can I find out how big an opponent's realm is?

Solution 1:

If you want to find out the size of a single realm, I would go the way bd33 suggested.

But if you want to get an overview of the sizes of all realms, go to ledger:

Then get to its tenth page (“Independent States”) and click on the “Realm Size” column heading to sort the list by that:

Solution 2:

Click on the Realm Tree on the right side of the character portrait of someone in the realm you want to invade.

There are two numbers: a percentage (relative strength, which you can hover over to see Levy numbers) and the number of holdings. Hovering over the bottom number reveals how many the individual holds (Demense) and how many their vassals hold. Go to the character at the top of the realm tree to see that information for the entire Empire/Kingdom/Duchy.