I highly suggest this excellent post by Debi Brim, experienced cake decorator and caterer, on How to Cut a Wedding Cake, including step-by-step photographs and instructions. I couldn’t have explained it better!
This “grid” technique also works great for how to cut a 3-D cake. Here I was below was using the same method. To summarize:
Remove accents or items that might in the way
Cut a strip of cake (in this case, it was about 2 inches wide). I cut downward until it hit the board. This was about 4 inches.
Then cut that strip into pieces (it can be 1″ wide pieces – I cut mine a little big here). If you want even smaller pieces, you can cut this in half again.
Remove the dowels/supports before cutting the layer below. (I use scissors to remove slippery dowels.)