What is the verification algorithm for verifying RSA signatures? I am not able to find much information how how to verify RSA signatures.

I have three values.

Message = "Launch a missile."


public key:

e = 010001 (this hex value equals to decimal 65537)
n = AE1CD4DC432798D933779FBD46C6E1247F0CF1233595113AA51B450F18116115


I want to verify if the signature below is the correct signature.

S = 643D6F34902D9C7EC90CB0B2BCA36C47FA37165C0005CAB026C0542CBDB6802F


The only formula I was able to find is 

$S^e = \operatorname{Pad}(\operatorname{Hash}(M))\pmod N$

Is this the correct verification algorithm? If so, I am unclear about the Pad() and Hash() functions.  How can I calculate the hash and pad functions?
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.