How do I get my deceased parents' house transferred into my name?

You probably need to file a small estate affidavit for both of your parents in the counties where they died. If your mother and father died with less than $50,000.00 in assets (not including their homestead real estate), you may file a small estate affidavit to transfer their assets to your name. It's unclear if you have siblings, but if you do, each of you will own equal shares of the property left behind. I recommend you contact an estate planning attorney to advise you on the specifics of your case. Good luck.