You have gotten some great advice so far. As already mentioned, it takes practice. I too am a scroll saw instructor. I start my students off using pine as it is cheap and easy to cut. But you will never get a smooth cut edge without sanding. Also if you stain it, it will come out very blotchy. 99% of my project are cut from hardwoods. With proper cutting techniques, you should never have to sand your edges. Especially with hardwoods. Woods like Maple, Cherry and Walnut come out with perfectly smooth edges that don't need sanding if you don't make any mistakes!
My advice to you is keep using pine for practice. Once you have some experience under your belt, start using some hardwoods. But, practice, practice, practice!