Locate his Will, hopefully you are named in it in an amount that at least equals or exceeds what would be your statutory share, and hopefully you are named in it as the Executrix so as to allow for you to represent his Estate, and if there is no Will, petition the Surrogate's / Probate Court for Letters of Administration and hope to have yourself appointed as the Adminstrator of his Estate. ANd only do this with a competent Estates and Trusts attorney.
If there is no Will, you will still have the right to live in the home as long as you want and are able (presuming you do not have a prenup that says otherwise). You will not, however be able to own it outright unless you receive gifts from his children or buy them out. You will be required to maintain the home while you live there.
You need a probate attorney right away. You cannot handle this yourself.