Fill in any holes or seams in the drywall before adding the textured mud. Use joint compound to fill the holes and to smooth over the seams. Dry, sand and repeat until the wall is smooth.
Mix together a batch of joint compound and water in a 5-gallon bucket, using a metal masher to combine them. Add the water slowly, keeping records of every addition so you can replicate the recipe for future batches.
Add fine sand to the mud and water mixture. Sand comes in various sizes, called meshes: the higher the number, the finer the sand. Obviously, using finer sand results in a finer texture that is not as obvious as the coarser mesh of sand. Mash the sand into the mud until you have evenly distributed it to get the texture you want.
Spread the sanded mud to the drywall surface using a 6-inch joint knife. Experiment on a piece of spare drywall to find a texture that you like. Some ideas include sponging the wet mud, using a paintbrush to create alternating brush strokes, rolling over the mud with a paint roller or just creating swirls with the joint knife.
Work quickly to cover one wall, as the drywall surface tends to absorb the moisture in the mud and dry it within a few minutes.