You can't. One of the first suggestions is somehow, without irony, to get another job.
MMM lives the life you can live on minimum wage IF you live in the right location and already own your home and can bike to work (you know, subsidized maybe by steady favors from being famous). Not so anymore since the new space, I think.
Actually living on minimum wage is probably a situation of living where you were born, not owning your home, not having favors from famous friends (or even parents and family), and having the additional cost of health insurance in a broken system (you can't afford MMM's HDHP and HSA on anything like minimum wage).
MMM is a testimony to living life with a badass view of money, not life on minimum-wage being a sweet gig for those stuck with it (unless you are already paid-up and retired and famous).
In
http://www.mrmoneymustache.com/2012/01/13/the-shockingly-simple-math-behind-early-retirement/, MMM argues that cutting spending is more valuable than increasing your income. He's right in terms of how it effects the mechanics of the retirement formula, but not at low-current-incomes. If you make 20k a year, you can't cut enough spending to make up for not getting to 40k a year, even though you could lifestyle-creep your way out of any progress at 40k a year, too.
The formula for a minimum-wage-earner to leverage being a badass is to:
1. sell absolutely all they have to minimize moving costs to get to a LCOL area with decent job prospects and maybe a month or two of expenses, looking for jobs they don't need more qualifications for (
http://www.mrmoneymustache.com/2013/07/25/50-jobs-over-50000-without-a-degree-part-1/). Unlike the article seems to imply, this is a strictly one-time opportunity. If they can cover a move AND an apartment by doing this (if they have enough stuff), they can actually skip to step 3, without the need to sleep in the car or shower at the gym.
2. screw up the courage to move first, or else apply remotely and pray for Skype interviews, but also apply to minimum wage jobs to string 2 together and prevent homelessness in the new area if necessary.
3. actually land the job(s) and take out a loan for a down on an apartment or sleep in the car/tent and shower at the Y, local gym, shelter, or recent acquaintance's place, saving every dollar for any job-related expenses (clothes, equipment, transportation) and/or repaying the loan, as the savings is probably gone.
4. acquire more skills like you have nothing else to do, and save a safety net so this is never so hard again.
And you'll STILL need the luck of getting and not losing any of those jobs before step 4. It helps to be good before waiting on luck. It also helps, while selling all your things, to look for jobs locally that may or may not pan out, and if one definitely pans out before the move, take it, and otherwise finish the plan. It's not a great time. It has a good (but not high or certain) chance of working, and it may also cost any left-behind networks and/or family ties. It's also obviously much harder with kids.