We want to create a multi-signature address with 2 components.
The first step is to generate the private keys and the public keys (addresses).
These are two public keys.
> 1NGJoYzwfMotjjBuZZ5H4BujcxGZMQDMoW (private key 1)
> 1L3pUofp8EYX7uXVFy2gNSBTanmdC8sRWe (private key 2)
We would take the private keys from both addresses (public key) and we would have to combine them.
(private key 1) & (private key 2) = multi-signature address (P2SH)
How would you do that without using software?
It seems like this has been discussed in the past with other addresses. Take a look at this post:
https://bitcointalk.org/index.php?topic=919430.0 (Post #6)
TLDR: It will take you a very long time to do it manually.
If you're trying to create an address to prove something to yourself I guess you could try but I would recommend using an air-gaped BTC generator like bitaddress.org or similar site. Head over the to their github page, download the code and run it on your own computer with the internet off. This would save you some time and get a guaranteed end result.