Not being married only means you no longer have 2 incomes with which to qualify for a loan. So you'd need to qualify strictly off of the income you have coming in. In general, the new mortgage payment (principal, interest, taxes, insurance) PLUS your current debts listed on the credit report should equal no more than about 45% of your gross income. So without knowing what the credit looks like or what the current debts are it's tough to say.
If you already have a house then you'll need to qualify with that payment as well unless you are planning on selling the house.
Only way to find out if you can qualify is to contact a lender and ask about getting pre-approved, which will include providing some income and asset information and submitting to a credit check.
Hope this helps!