There are many things you can do to improve your credit score right away. Begin making early payments on your credit cards that are over the minimum payment. Take out a secured loan, even a small one at your bank and then use it and pay it off right away. Consult with a credit counselor for more advice. You will be in a much better position to get a mortgage the higher your credit score is! Good Luck!
I am not a loan officer so therefore can't answer this one. The clients I have assisted have had 580 and lower and some of it was due to poor reporting on the 3 credit bureau. Start there and you can do that yourself for free with your annual credit report. It's hard to unravel a credit problem once it has been reported wrong sometimes it keeps popping up on another reporting agency. Once you find out why the score is low then work on that area.
If the problem is delinquent credit issues get back on track with a strong budget. That is the quickest route to legally bump scores unless there are mistakes or lack of open credit lines. Unless you have three or four open trade lines that are paid as agreed for about a year the score will probably stay low or go even lower.
Check your credit card balances; this is the most frequent problem I see on credit reports other than delinquent accounts. If the balance is at or near the limit on the account it will crush your credit score. Pay them down as much as possible, especially the ones with very low limits. They hit your scores as much as the big ones so your payments will have more impact on the little ones. Your question does not contain enough information for anyone to offer specific guidance that will put you on the fast track. I am rather booked up until Thursday morning, would be glad to look at your details after that if you still need help.
All the answers have good advice; the bottom line is you need to first speak to a lender. Find one that you're comfortable with (your Realtor can give you a few names) and talk to them about how to bring your score up as you look at what is currently available and as you're shopping for your home. There are so many things that are considered, but there are also many programs to help buyer. Get the facts now and start the process.
Not knowing any of your finances/assets--visit with any qualified loan officer(s) first, see exactly what your budget can handle and check your credit score--their scoring is different--Currently FHA loans do require a minimum score of 620 and 3.5% down, however there may be some lenders willing to work with a lesser score, but the interest rate may be higher.