Removing sawdust is an important step before staining, painting, or otherwise finishing a wood project.
Step 1: Wipe with a damp microfiber cloth
Sawdust just loves to stick to a slightly damp microfiber cloth. Use just enough water so that any left on the wood will quickly evaporate.
Microfiber cloth is better than tack cloth becauuse it's reusable, and it doesn't have a nasty smelling, sticky chemical agent all over it.
When you wash the microfiber cloth, keep it away from cotton.