What do I do to buy the house in foreclosure that my parents’ left to me if my name is on the foreclosure?

It is not clear what stage of probate and foreclosure you are in. How long ago did your mom die? Was there a proceeding filed in the Probate Court? If so, has the court already ordered the transfer of title to you? If the title has not yet been transferred, you have to determine whether the home loan is "underwater," that is, the remaining loan principal exceeds the price the house could be sold for. If it is, you should probably refuse the inheritance. If the loan has equity (value exceeds principal) and you want to keep the property, then you will have to make a deal with the lender to pay off the loan balance or, if the lender will agree, pay just the amount necessary to bring the monthly payments current and continue to make payments yourself.

You should try to negotiate with the entity which is handling the foreclosure. The difficulty is determining who actually owns the note and/or mortgage. Also, if the foreclosure is nonjudicial, then it is extremely difficult to be able to locate and attend the purported "public auction" in order to make a reasonable bid after the foreclosing entity may have ramped up fees and costs which inflate the amount that it would take for a bidder to purchase the property.

It depends on the state of foreclosure; whether there is a probate; who is the administrator; how the title to the house was held.