If our Sun could become a black hole, the planets would continue to orbit around it the same as they do today. Recipe for a Monster Einstein's theory of relativity describes gravity as a curvature of space-time. The more massive the object, the greater this distortion. Black holes are so massive, that they distort space-time into a deep, bottomless well from which nothing can escape. Black holes are actually formed from super massive stars whose mass measures at least ten times that of our Sun.
Stars burn hydrogen in a process known as fusion.
This nuclear process produces pressure that pushes out from the center of the star. This pressure counteracts the force of gravity which pulls in. The two forces are perfectly balanced. This prevents the star from collapsing or blowing apart. When the star exhausts its supply of hydrogen fuel, this balance is upset.