If you are just beginning the long road to paying off your debt, you need an emergency fund in place. Your emergency funds will keep your sticky little hands off the credit cards while you pay them down.
So how do you save up an emergency fund (or two)?
Like everything in life, it's better to set a clear goal. "I want to save some money" isn't very helpful. "I want to save $500 to keep away mini-emergencies" or "I want to put three months of expenses in a savings account" is much, much better.
To save for your mini-fund, start by taking a look at your budget. See where you can trim a little. Skip after work drinks, opt for the laundromat instead of fluff 'n fold, pack your lunch a few days. Keep track of what you save.
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Move those dollars saved into a separate account and DO NOT SPEND THEM until you really, really need to. How will you know? It will be a time when you would have used your credit cards, like for a surprise car expense or a shockingly high water bill. A sweater that is on clearance is not an emergency, no matter how good you look. Sorry.
Ideally the savings account will be easy to access, but not too easy. Think online (FDIC insured, of course) accounts that link to your checking. They usually take 2-3 days to get the funds in order.
Use the same steps to set up your big fund, but this time see what items on your budget you could really cut if you had to. Say you lose your job and unemployment isn't an option for you. More than half of working Americans live paycheck to paycheck and fewer than 1/10 of those people have any savings AT ALL! What would happen to you if you lose one paycheck? Two? Three months' worth?
This isn't exactly fun to think about but it is important to consider. Whatever your pared down version of life would look like multiplied by three is the amount of money you need to get you started.
Once you've got your number, get to work! Save until you've reached your goal. And hope you never have to use the money, but feel better knowing it's there.