Most banks will lend around 80% of the homes equity. So take what you would sell your house for divide by 80 and subtract what you owe. That is probably around what you will qualify for. Credit and debt to income plays a big part in the descision process. They also take into consideration how much the loan will lower it to.
Be sure you shop around. Get fee lists from the banks. Rates, application fees, PMI, points, closing costs, appraisal fees, pre-payment fees and yearly fees to start. Be an informed applicant, you dont want suprises.
Also, be honest. They are gonna pull your credit and see everything anyway, save them the work. If they call you saying they need more information do what you can to get it to them as soon as possible.
Hope this helps.