How would my brother transfer the deed to his house to my name?

He would prepare and sign a deed, listing himself as seller and you as the buyer. Then you would have the deed recorded in the county clerk or county register's office.

Is there a mortgage? Might there by other liens on the property? These things make a difference. I suggest that you and your brother have this done by an attorney or title company. It is inexpensive and you'll know that it was done properly. If you try to do it yourself and make a mistake then it can be very difficult and costly to fix.