Butter an 8x8x2 pan. Then line with wax paper or plastic wrap. (I prefer wax paper)
In a double boiler* - combine sugar, milk and butter – stir until it boils then stop stirring-cook until 238 degrees F on a Candy thermometer or softball stage. Remove from heat- add butter and vanilla and beat with a wooden spoon until glossy-this is the part where they are scraping and turning with a wooden paddle on a marble board. Do not under beat. Poor into pan and cool. Cut to preferred size.
*Invest in a double boiler for making fudge. Using a water bath (fudge pan inside a larger and with steam/boiling water) to heat the fudge keeps the chocolate from scorching and or sugaring.
Also a good candy thermometer if you choose to make the kind without sweetened condensed milk.