It might be best to work directly which each card company. They will offer you terms you may not even known were possible (waive penalties, extremely low interest rates, possibly credit back a portion of previous charges, etc.). What they can offer or put in exceptions for depends on a number of things.
I wouldn't advise of a debt settlement agency. What they do is hold your money until they are able to negotiate a bare minimum percentage of your debt. Meanwhile, your debt is going further and further past due and damaging your credit. Just before it gets ready to write off (a major blow to your credit) they make their move. Some people don't know this but you can settle directly with card companies if you run into a large lump some of cash and probably won't be able to make monthly payments afterwards. Sure the percentage won't be outragishly low but the hit to your credit won't be near as bad.
Credit counseling agencies are ideal for people that have many, many cards. If you have just a few cards or just one, work with that card company first.
You can expect them to ask questions about your net income. They will ask questions about expenses such as rent/mortgage, car payment, student loans, and other revolving debt. They will use this to find your income to debt ratio. They want to make sure you can afford a lowered payment (some people think it looks good to have more debt than income but it's the opposite). Be honest and very open. They are going to ask stuff you might think is none of their business. They need to know because if you can't afford other things, they know you'll probably fault out of the program. It's a commitment and plan to commit to a fixed amount for a long period of time. Going through a credit counseling program or doing most programs through card companies usually closes your account.
Source: I worked with business credit cards.