Yes, credit problems aren't going to look good when an airline does a background check, but it isn't the end of the world. Basically, you just have to pay back what you owe.
Here's what you want to do. First you need to figure out why you went delinquent on some accounts and fix the problem. You'll need to get spending under control and organize your bills. Starting from today never pay anything late. If for the next two years you never pay anything late and keep a few accounts current you're credit will improve significantly.
The next thing you want to do is get a copy of all three of your credit reports. You'll find links at the bottom. What you need to do is to find every negative account that you owe money on. Then contact the business and see if you can pay it off or agree to a settlement. Make sure you get everything in writing. If you make an agreement make sure it is written and signed by a company rep. Typically, depending on how old the debt is and the company that you are dealing with you may be able to talk them into a lower payoff amount, or negotiate to get the negative information removed from your credit report. Just remember that if you settle for a lower amount the IRS considers the part you didn't have to pay income, and you'll pay tax on that.
Your goal should be to get every negative account on your credit report down to zero, and to keep current on the accounts you have now. This shows that although you were irresponsible in the past, you took care of is and now you've cleaned up your act. Also, remember that after seven years accounts are removed from your credit report. In seven years it could be completely clean, unless you declared bankruptcy.
Here are the links to the three credit reporting agencies.
http://www.experian.com/
http://www.transunion.com/
http://www.equifax.com/
