Stick with a game long enough, and eventually the PCs are going to enter into the realms of power where they're the movers and shakers of the world. Long before that, the entrepreneurial PC will likely have more money than they know what to do with, and a truly entrepreneurial PC will have more businesses than they know what to do with - all of which funnel them more money. The point being, go long enough, and the PCs are going to have their own minions around to help with things. Maybe it is just a few knights to guard the home castle and do the odd random quest. Maybe it is a complete corp of mercenaries that can be rented out to the highest bidder. Either way, not many games are equipped to handle what comes next easily and efficiently. So, let's see what we can do about that.
Step 1: Don't Panic
The first thing you need to do when your PCs start looking to hire minions and underlings is to not panic. Honestly, your PC has just given you a huge thing to work with, and that is good. Always remember that as the GM you can always resort to the old hand wave to handle things. It may seem a little cheap or backhanded, but, ultimately, there is nothing wrong with it. You are the GM after all, this is part of the job description.
So, worst case scenario, the PC comes up to you and wants to use their minion army to attack Baron Von Plot Villain's castle. Just smile, make a die roll or two for the minions' leader (unless a PC is leading the fight, but that is altogether a different scenario) and let them know what happens for good or ill. If nothing else, you can do this while buying yourself time to figure out how you want to handle minions in the future.
Step 2: A Question of Depth
Alright, so we're not panicking and have defined our fall back position of the old hand wave. What's next? Well, next we want to look at just how in depth you want to go with the care and maintenance of your PCs minions. Are we just hand waving the details of feeding, clothing, arming, and training them as things done by other people with money set up for it? Or is managing those costs and times going to be a factor for the game? Keep in mind that the more in depth you want to go, the more work you have to do. Also, that if you go too far in depth you are essentially adding a second game's worth of mechanics to the mix. This is perfectly fine if that is what you want to do, just be aware of the can of worms you may be opening.
Luckily, a number of systems that are built for this kind of thing are out there for you to peruse and see what you can take. The classic system for running countries and estates is Birthright, but other systems also tackle the "PCs have holdings and minions" card in a variety of ways, such as Houses of the Blooded, Blood and Honor (same system as HotB), and Pendragon. So, if you need ideas on handling the in depth part, check out how other places have done it.
Step 3: Care and Feeding of your Minions
You've decided that you want to get at least somewhat involved with the costs of raising minions in your game, and why not? Why should the PC just get all the benefit and none of the cost? Raising an army of minions is costly, and isn't something PCs should jump into super lightly. Now, there are problems here though. Namely that, unless you and your friends are economics enthusiasts, that the amount of book balancing here is going to be mind bogglingly dull. Instead, I recommend using something like the Profit Margin system from Fantasy Flight's Rogue Trader system.
Profit Margin is a stream lined system to handle the economics of running a large ship in the 40k universe. Deals made have either a positive or negative effect on a ship's profit margin, and a Rogue Trader can see about how well they're doing wealth wise by that same margin. Things bought with profit margin don't just get the item (if it is a permanent cost), but also covers things like the maintenance and general care of the piece of equipment.
I like Profit Margin for this, because it is abstract but effective. It cuts out a lot of the BS, "this is what you have after covering all of your costs". Now, granted, you're going to have to do work converting your games economy scale to profit margin, but the work can be worth it. Then, when a player wants to hire five more guys you can simply tell them "That'll cost you 1 point of profit margin per month, and be at least four months before you can give them jobs to do."
If you do do this system, I'd recommend keeping it separate from the parties normal resources. Yes, the PC will want to dip into his stash now and then, and that is more or less fine, but keeping it separate also helps keep your sanity. Especially since it means you can do less converting of the games money system to profit margin, letting you keep "regular flow" and "irregular flow" separate.
Step 4: Minions on the Job
So, we've handled all the book keeping and decision making, now it is time to send those minions out to work for the PC and earn their keep. Only, how do you handle that? Do you make them their own stat sheets and play it as a session? That could be fun, but kind of defeats the purpose of using minions to stream line things. Do you just go back to handwaving? That seems a bit arbitrary after all the other work put in (but is still fair). So, what do you do?
Honestly, and perhaps unsurprisingly, I'm going to recommend Unsung Heroes for this. It isn't very large or robust, but it enables a large number of things to be handled fairly quickly, and is specifically designed to handle those minions and other faceless people that are present but not the heroes at all the major events.
I am not sure if there are other systems that give minions their due, or a quick way to handle them, but if you don't want to use Unsung Heroes, then I'd recommend some arbitrary rolls. Assign the minions dice pools/skill bonuses as befitting their abilities (probably lower than the PCs), and give them a success/fail roll for the mission, and then another for if they live/die (assuming mission is dangerous). This lets you handle things a bit more personally.
Step 5: Rinse and Repeat
With that, you've got about everything needed for handling minions covered. Rinse and repeat the steps as needed to handle it, and watch as your PCs become more entrepreneurial as they see that you aren't opposed to it. Of all the steps, the most important is step 1. Don't panic, and if you need to, don't be afraid to hand wave a problem away - or into existence.
Did I miss anything? Other thoughts, questions, or points to make on this? Sound off in the comments