As someone who has been a lender and worked with lots of good people with tough credit, let me suggest your first step is to work on your credit. Whether you will qualify now or not better credit opens up more options and lower rates & fees.
A few years ago it seemed that anyone with a pulse could get a mortgage. Then too many people did and we have had the collapse of the housing and mortgage industry. These days there are few options for people with tough credit, the primary option is FHA.
FHA is available through all major lenders and most mortgage brokers & bankers.
If you choose to work on your credit first, my general advice is to establish and live with a budget for a while. Anticipate expenses like car maintenance & repair and budget for it. Build up as much savings as possible, more down payment equals more lending options. It will also insulate you from unexpected expenses.
Next, obtain a copy of your credit report from each of the reporting agencies, Experian, TransUnion and Equifax. You do not need to pay for this and you do not need to sign up for any services. Dispute any issues you find which are in error. Sometimes credit reports are inaccurate and until you correct the record, no one knows. Write letters to each agency disputing anything and where possible provide proof. Fixing Experian does not fix TU.
There are mortgage lenders who will assist you with the credit repair process and advise you as to your options. Consider some who answer here or talk to some local lenders.