Because butter contains milk deposits it can burn easily, so it can be a temperamental cooking medium. Adding some oil (which burns at a higher temperature) to the cooking pan with the butter can help get around the problem. Alternatively, clarifying the butter will make it more stable. For baking, pale, creamy unsalted butter (sometimes called 'sweet' butter) is better than unsalted butter as it allows the cook to control the amount of salt going into the finished dish.
You can make your own butter at home with just cream and a jam jar. This activity will take a little patience and some stamina in the arms as you shake and shake the cream in a jar, but it will all be worthwhile when, quite suddenly, you're shaking a lump of butter.