The decision to finish your own unfinished pine dresser may be the best if you are trying to achieve a specific color or if you are trying to match the piece to something you already have. Many stores and companies sell solid wood furniture right next to their sales floor or from a catalog that is completely bare of any stain or finish coat. This leaves you open to all the possibilities of creativity.
Before you start, find a well-lit and well-ventilated place with a large amount of airflow. Basements with large windows that can be opened or a clean garage when the temperature stays around 65 degrees work well. Remove all the unfinished bedroom furniture from the cabinet and the number of them on the backs so you can make sure they are put back in the same position. Find an old piece of cardboard or a shoe box lid. Drill the screws of the controls through the cardboard and screw the knobs back to the screws.
If the pine dressers cheap you are finishing is a hardwood such as oak or maple, use a 150 grit sandpaper and lightly sand the dresser, just going in the same direction as the grain. If the cabinet is a soft wood like pine or alder, the use of 220 grains of sand, always goes with the grain. With a sticky cloth, go over the entire dresser generously, picking up all the sanding sawdust.