Question: What is a better way of saying "in order to demonstrate this, I will..."? I already use "to that effect" in the same paragraph. I'm looking for something as compact and concise as "to that effect" that will also be a good transition for the beginning of a new paragraph.

Answer: 
Perhaps "To illustrate this, I will...", "Demonstrating this, I will..." or "As an example,.."
Is the sentence in question immediately followed by the character actually performing the demonstration? In that case: 

"Observe."
(Does thing). 

However, the whole thought "in order to demonstrate this, I will..." might be completely unnecessary. If the character already talked about the thing, just having them do the thing should save words.