An emergency fund is a necessity for everyone, whether you're trying to work your way out of debt or you've never had any debt.
In putting my financial situation into perspective when I first became interested (and aware) in my personal finances, and after reading Dave Ramsey's The Total Money Makeover: A Proven Plan for Financial Fitness, I knew that an emergency fund was something that I needed to have if I wanted to get my finances under control. However, I didn't create one right away; instead, I put mounds of money toward my high interest debt. Was this my best choice? It worked for me (as I didn't have any unexpected expenses during that time period), but it was certainly a gamble, and not something I would necessarily recommend to others.
For me, I couldn't stand to see the interest on my credit card debt continually and quickly larger. So I started attacking it. However, if I had had unexpected expenses, I would have put myself into even deeper credit card debt, because the only way I would have been able to pay for these unexpected expenses was with a credit card. Very luckily for me, I didn't.
How might you go about starting an emergency fund? Well, after you've created your budget and have all expenses accounted for (including minimums on loan and credit card payments), you take the remaining income and put it into a savings account, where the money is liquid. I recommend SmartyPig (http://www.smartypig.com/), as this yields the highest interest rate that I've been able to find for a savings account.
Each pay period, or with any additional income you receive, put it into the emergency fund until you've reached $1,000. This is a very good starting point for your emergency fund, and this will allow you to pay off most emergencies without putting yourself into further debt. Once you've accomplished funding your initial emergency fund, you can begin to aggressively pay off your debt. This is a very good step toward getting yourself out of debt and into a good financial position. The road ahead may be longer than you'd like it to be, but by making responsible financial decisions like having an emergency fund, it's a road that will be shorter than you think.