There are lots of good tips here, involving budgeting and setting goals, so I won't repeat them. Here are a few others. I apologize in advance if this sounds like lecturing, but since I've been there myself I thought I'd be direct.
--First, make sure you and your husband are on the same page with whatever decisions you make. Otherwise, your plans are much more likely to fail.
--Cut, cut, cut your expenses. Read all the previous suggestions (cable, magazine subscriptions, movies or video rentals, coffee-shop coffee, eating out, cell phones). No new clothes, no trips, no little luxuries for you, your husband, or your kids. Yes, it's painful, but it sounds like you're living paycheck-to-paycheck. And only you and your DH can decide what you can cut; my list simply contains suggestions.
--Establish a strict budget and stick to it. As I've suggested above, the budget has to be for all members of the household. Important mental tip: don't think of it as a deprivation budget. For every dollar of debt you pay down, you're investing in a stable, happier, more rewarding future for you and your family. To help you commit to this budget and attitude, make a big poster that helps you chart your progress. Or a goals list. Or whatever inspires you. But make it real by committing it to paper and making it public (at least within your household).
--Do not play credit-card roulette, using your credit cards to help you manage your debt by juggling the balances. People often think they can play this game just temporarily and, for most people, it just makes the problem worse.
--In fact, if credit cards are a major source of your problem, stop using them altogether. I know this can be easier said than done, but I found it was necessary for me.
--If you can, try increasing your deductibles on your insurance. It's a bit of a risk if you don't have spare cash, but as mentioned above, you already sound like you're living paycheck-to-paycheck and you need to make some drastic changes.
--Once you get into a position to do so, send out your credit-card payments as soon as you get the bill, if not sooner. If you can, send out more than one payment a month. That way, you're chipping away at the principal and earning less interest. (Follow other posters' suggestions on paying off the highest interest card first.)
--Simplify your life and streamline what you can. Sell things, barter things. Trade your car for a less expensive model, if that's a big expense.
--As a full-time student, you might have access to campus jobs that might be appealing to you because they're so part-time, a few hours a week that you might be able to squeeze in. Working in a school cafeteria, for instance, isn't glamorous, but sometimes they'll hire someone for just a few hours a week. Or the library. Or an office. Now, I don't know your schedule, but it's possible you have a break between classes where you aren't taking care of your children, you might be able to get that type of job. Of course, you need to balance that with your studies....
--Also, speaking of college, you might see if various departments are offering a few bucks to participate in various studies--low-risk psych studies, behavioral modification studies, etc. They may only pay $5 or $10, but often take only an hour or two, cash in hand.
--Could you babysit another child or two in addition to your own? I'm not suggesting you start a daycare business as you're in school, but even offering your services to other parents if they want to have a night out might be a way to bring in a few dollars. Or perhaps you could start a babysitting co-op that allows you and other moms to get part-time jobs?
--Last but not least, take care of yourself mentally and physically. This kind of stress wears on you, so you have to be extra careful to do good things for yourself. Get enough sleep, eat healthily, exercise.