This is not tax or legal advice as there are a number of factors which go into answering this question with certainty. However, if you received the property by gift (which you did if you paid "$1" for it) you received no step-up in cost basis for the property. This means that when you sell it, your proceeds (your half) will be subject to capital gains on the difference between the sale price and the cost basis of the property when you received it (in other words, your parents cost basis). I say subject to capital gains - this means that you have to properly analyze the situation to determine if you will have a tax burden due to the sale but it is likely you will. Retain a qualified accountant to assist you when preparing your taxes for the year the property is sold.
This is not legal advice nor intended to create an attorney-client relationship.
The previous attorney accurately described how you figure your gain from the sale of the house. The "cost basis" is, essentially three components:
1. What your parents paid for the property;
2. Improvements made by your parents to the property; and
3. Improviements made by you and your sister to the property.
Then, you take your half and she takes her half. Because you have lived in the house, you will probably be eligible to exclude up to $250,000 of any taxable gain ($500,000 if you are married filing jointly).
What confuses me is your statement that the house is "worth nothing". How can that be? If so, why would there be a sale? Wouldn't you just give the house away as it is worth nothing. It just makes no sense. If the house has a mortgage, and its value is equal to or less than the mortgage balance, the house itself is still worth something, even though you may walk away with no cash.
See a qualified CPA.
Marty Davidoff, email@example.com, 732-274-1600. This answer is provided for general information only. You should seek advice from an attorney or tax professional.