This section is taken up with two main topics: acquiring henchmen and the loyalty of henchmen (and hirelings) once acquired.
Before we get into that, though, I want to point out something that comes up a few times in this section: why henchmen sign on with PCs. Gary is clear that henchmen sign on with the PCs because they aren't doing well on their own; henchmen are professional adventurers who are unsuccessful, for whatever reason. This explains why the PCs must provide equipment for henchmen and why only first level henchmen will be attracted to PCs of fifth level or below; if they were doing well enough to have advanced in levels or even well enough to keep or provide their own equipment, they wouldn't be desperate enough to apply to be another adventurer's follower.
Gary first outlines the steps that must be taken to acquire a henchmen. Basically, the DM must first determine how many henchmen are available wherever the PCs look, and of what race. Gary is extremely vague here, throwing out some rough numbers (one prospective henchman per 1000 people), but then advising that they should be adjusted situationally… without providing guidelines on how to do that. (ACKS, which it's basically impossible not to compare these sections of the DMG to, is immensely more helpful, detailed and streamlined here.)
After the DM has done this, the PCs must advertise, spending their money posting notices in public, hiring criers, hiring agents or going around to taverns and inns, buying rounds for the house and paying barkeeps to send potential henchmen their way. Each of these methods cost different amounts of money and have different rates of effectiveness – that is, the percentage of actually available henchmen that will hear and actually be attracted to apply to join up with the PCs. Using more than one method decreases the over-all effectiveness of all methods used (du to "overlap"), but not by enough that it isn't theoretically worth doing if you want to have a wide choice of henchmen.
Once that number of potential henchmen who will respond and apply has been determined, they begin to show up at whatever location the PCs indicated they would take applicants over a period of 2-8 days. The PCs interview them, but must be careful not to ask questions about religion or alignment or to frisk or search them or cast any magic upon them except for Know Alignment or Detect Good/Evil, as these will probably offend the potential henchman and make him unwilling to join the PCs. There doesn't seem to be much justification for this, especially in a world where crazy evil/chaotic characters are likely to be infiltrating parties for their own or a master's nefarious ends; this possibility actually strikes me as exactly the reason why Gary banned inquiries in this direction. The personality and other characteristics of the prospective henchmen should be rolled up on the NPC traits generator further on in the DMG.
If the PCs want to hire the prospective henchman, they make an offer and the DM rolls percentile dice; if the roll is at or under a percentage determined by how good of a deal the PC is offering and the PC's charisma modifier, the prospective henchman accepts the offer and is now a henchman. (It was interesting to me that ACKS leaves the specifics of this up to the judge, but LotFP:WFRP actually has a short, simple list of modifiers that are quicker to tabulate than AD&D's. I'm unfamiliar enough with Basic D&D not to know whether that's something LotFP inherited or if that's just another of Raggi's mechanical innovations that is overlooked because of the atmosphere of LotFP.)
Gary then moves on to the loyalty of henchmen and provides a good page or more of variables that affect henchman loyalty. Unlike D&D systems for morale and loyalty that I've seen that use a d12 or 3d6 system, AD&D uses a percentile system; henchmen begin at 50% loyalty and that score is adjusted as situations arise and conditions are met. For example, on the extreme, if a PC kills a faithful henchman in front of witnesses, that's -40% to the loyalty score of any henchmen from that point on. If a henchman has known or been a follower of a PC for more than five years, that's +25% to loyalty. If the PC is Lawful Good in alignment, that's +15%, but if the henchman differs from the PC in alignment by two places, that's -15%, and so forth.
Finally, I find it interesting that Gary allows for the PCs to recruit NPCs they've captured as henchmen. This is a rule I don't think I've ever heard about. It's the once exception to the rule that henchmen come unequipped and also seems to be the only way to get henchmen that are higher than third level – henchmen (or associates as Gary calls them, presumably because they will rank and be compensated on a comparable level to that of the PCs) acquired this way may be up to two levels above the PC recruiting them, though they will only stick around for one or two adventures. If prisoners are forced to join the PCs, they will have very low loyalty, but if the prisoners are offered very good terms and given a genuine choice, they may sign on as permanent henchmen with a good loyalty level.