What is the verification algorithm for verifying RSA signatures?
I finally found an answer to this.  A simple formula to verify the signature is: $M = S^e \pmod N$.

If I take the numbers in my original post and plug them into that formula, I get $M = 4C61756E63682061206D697373696C652E$.

Then, if I use the python command below to convert the hex string back to ASCII, print("4C61756E63682061206D697373696C652E".decode("hex"))

I get "Launch a missile", which is the same as the original message.  This means I can verify the signature was correct.