Is the way a man in the middle attack works, is that he can see that these two users are transferring files, and somehow pull the data stream to himself from both ends? Can he do this on an already ongoing file transfer session?
You need to define a threat model. The usual suspects are message insertion, deletion, tampering and reordering. Sometimes the attacker only needs to tamper with a message so you do the wrong thing. For example, he/she may need to flip a bit so "transfer $100 from A to B" changes to "transfer $900 from A to B". In this case, the attacker did not need to be in the middle or decrypt the message.
I'm trying to understand the way MITM attacks work so I can see if I can protect my program from such attacks... but if the only way to reliably do so is to use a certificate authority(of which I'm still learning about), please go ahead and tell me that.
Rather than attempting to design a hardened protocol, perhaps you could use a protocol that already exists that addresses your concerns.
That protocol would be Z-Real-time Transport Protocol (ZRTP). The protocol is specified in RFC 6189, ZRTP: Media Path Key Agreement for Unicast Secure RTP.
ZRTP is a key exchange protocol that includes Short Authentication Strings (SAS) to keep out the MitM. Essentially, the SAS is a voice authentication that only needs to be performed once. You can omit the SAS check, though its not recommended. If you omit the check and the bad guy is not attacking, then everything is OK for current and future sessions.
Once you establish your first secure channel without adversarial tampering, all future sessions will be secure because of the way key agreement for the current session depends on earlier sessions. And the earliest session (first session) is known to be secure.
ZRTP also provides forward secrecy, so a compromise of the current session does not affect security of past sessions.
ZRTP does not require certification authorities or other (un)trusted third parties.
Dr. Matthew Green has a blog about ZRTP on his Cryptography Engineering site at Let's talk about ZRTP.
To answer your question about MitM, there's too much for a Stack Overflow answer. A great free book is Peter Guttman's Engineering Security. MitM is sometimes a goal of an attacker, but it not his/her only vector. Guttman's book looks at a number of threats, how humans act and react, why the attackers succeed, and how to design around many of the problems.