There are essentially two things that potential lenders can learn about you from a credit bureau: Your credit report, and your credit score.
The credit report includes all the facts the bureau knows about you. It includes the total owing on all your cards, the total amount of loans you have, lines of credit, and so forth. Significantly, it probably does NOT include your mortgage, unless you have defaulted on one. That's because banks tend not to report their mortgage business to the credit bureaus, and so the bureau's don't have it.
The score part of your report is interpretive, and actually "score" is misleading. There are LOTS of different scores. The scores are produced by adding up all the different facts in different ways, calculating various ratios, and all sorts of other fancy things. Big lenders, like banks, often make up their own scores rather than choosing from the scores provided by the bureaus.
In terms of cleaning up your credit, as everyone says, it takes seven years for a negative mark on your report to grow old and expire. The right thing to do is try and consolidate all debts into a single debt. This is essentially what a credit counselling agency will do for you. You can do it yourself if your credit is not totally crap: Go to your bank and take out a line of credit or a loan and use that new debt to eliminate all the other debts. Make sure the new loan has a reasonable payment plan, and make the payments.
Doing the above has two effects: First, you get a lower interest rate. The bank loan/line will have substantially less interest than a credit card or store creditor or unpaid tax debt would have. Most creditors will charge you 1 or 2% per month on unpaid balances, which works out to 12-20% per year. The line of credit will charge you 5-10% depending on your situation. Second, despite the fact that you are still in debt, you now have no bad debts. You still owe just as much, but you have paid off all the debts save the new loan, and you have made every payment so far on that new loan. Your credit will immediately improve; though you will still be a fairly long way off from getting it all cleaned up and having "good" credit.
Your credit improves for two reasons: First, you will have fewer debts, fewer credit cards, etc., and that is commonly a part of your score. Second, everything you do have is in good standing. Of course, you have a bunch of late payment notes, and those take time to expire, but they are not as bad as having an outstanding default!
It's possible to clear bad marks completely off your credit report faster than seven years, but it's tough. Essentially, you have to convince the credit bureau that the bad mark on your credit score was actually an error: Not only have you paid back the loan satisfactorily, but the previous "default" was actually not your fault. This is usually tough, especially if it really was your fault.
Sometimes you can succeed, especially if you can convince the creditor to side with you and write a letter to the bureau stating that it was all just a misunderstanding. Even then, expect it to take six months for the bureau to "investigate" (ie: drag their feet) before it actually comes off your record. If you can remove a few items from your report--especially newer ones--it'll help. The advantage in removing newer ones is obviously to hasten the 7 year waiting period before the last bad debt disappears over the horizon.
Beware of fly-by-night scam operators who try and rip off people with bad credit. Some con men operate on promises that they can clear your credit up magically when in fact they can do no such thing. Worse, some will try and extract money from you claiming that they will use it to consolidate and pay off your debts for you--when in fact they just disappear with all your cash, and you are now further into default and deeper in debt.