Once your home goes to auction, it will either go back to the bank or someone will buy it at auction. If it goes back to the bank, you will be notified by someone that has bank authorization that you have to vacate the property. Depending on circumstances, you may even receive a monetary incentive to move. You will have some type of notice to vacate but if I were you and I knew this was happening, I would be preparing myself and my home by doing packing and getting ready so that you are not under additional stress when you do get notice. I cannot give you any idea of what time limit you will have.
If a private party purchases the home at auction, you will be receiving notice from them also about vacating the premises. If you have questions as to what your legal rights are, I would either talk to an attorney or see what information you can find out through state offices that deal with rights of property owners.
It is sad to have this happen. Most homeowners are unaware that if they are getting behind on their payments that their best option is to put their home up for sale and work with the bank in getting the home sold. This is the best way to alleviate the debt and have the least amount of damage to your credit. If you know people who are in your situation, please relay the information on that they should call a licensed real estate agent to discuss their options.