Basically what happens depends on how new the scheme is. If it is only started being advertised, then there is usually a period for passengers to become used to it, with warnings being given. After 2-3months, Byelaw Enforcement/BTP will start the crackdown on whatever byelaw it is.
The offender will be given a caution:
"You do not have to say anything, but it may harm your defence if you do not mention when questioned something which you may later rely on in court. Anything you do say may be given in evidence". That type of caution is used to inform a suspect that anything they say from that point on will be officially recorded (written) and could be used as evidence in court, and is not a formal police caution. This forms part of the Police & Criminal evidence act, (PACE).
Generally, unless they have good reason to have breached the byelaw and provided a valid reason to the enforcement officer, they will be issued an immidiate summons. They will appear in Magistrates Court, charged with an offence under the Railway Byelaws. My own experience is that people charged with Byelaw offences usually are found technically guilty. It is usually arguements over 'there were no warnings' etc which are given up as defences.
Either way, any TOC doesn't have to give you a second, third or how ever many chances. Many don't, in fact most won't.
No TOC that I know openly publishes their procedures, and taking into account that every case is different, I doubt there are any 'offical procedures' other than how the enforcement officer at the time deals with the incident.
For purposes of this thread, "enforcement officer" can be anyone trained to PACE standards acting as an agent for a TOC, so security guard, police, ticket inspector.....