The topic itself is too huge to know how to help you specifically without more details of your own personal scenario, but generally speaking a healthy credit score is attainable as long as you have at least two or three open and active trade lines; whether they are credit cards or installment loans is up to you.
If you don't have any open credit accounts; get them open ASAP and be certain to pay your bills on time and manage the accounts wisely! (don't max out a new credit card!)
Both of you need to understand that your bad credit is a direct reflection on you and it's going to impact your lives negatively for years until you suck it up and do the hard things you need to do in order to improve it.
You need to put away your credit cards and stop using them entirely. You need to start paying down your debt regularly every month and living well beneath your means this year. I would encourage you to visit the website: http://www.nchfa.com/ where you can find some credit counseling and mortgage assistance.
Your credit didn't become as bad as it is overnight and it won't get repaired overnight, but if you'll commit to a year for focusing on the issue and working to fix it, then this time next year I believe you'll be in a good place with good credit. I wish you all the best and a successful 2013