Step 1: Remove all hardware.
Remove all hardware, including drawer pulls and metal decoration on drawer fronts. If you are going to reuse the same hardware, bag everything up so that you don't lose any screws or handles.
Detach the mirror, if one is attached, by removing the screws holding it in place. Lay it flat on a drop cloth.
Step 2: Apply a chemical stripping agent.
Using a water-soluble stripping chemical allows easier cleanup once the paint has been lifted and scraped away. Work in a very well-ventilated area and always wear a mask, eye protection and rubber gloves while working with the stripping agent. Apply it to one small area at a time and leave it to sit for the time specified on the label (this will vary by brand).
Once the paint lifts and bubbles, scrape along the woodgrain with a plastic putty knife (wear your gloves, eye protection and mask). You may have to apply the agent multiple times to the same area to remove all of the paint. If you have used a wash-away type of stripping chemical, you can rinse your piece with water to remove any residue. If you have used another variety, follow the manufacturer's directions for cleanup.
Step 3: Sand.
Once you've removed all visible paint, use a fine-grit sandpaper and sand your entire piece along the grain. You can use a palm sander to cover a large amount of area faster, but you need to do corners by hand. Use a soft cloth to remove all sawdust.
Step 4: Stain.
Choose your desired finish and apply over small areas at a time with a soft brush in even strokes, going with the grain. Use a soft cloth to remove the excess stain while it's still wet. Repeat the process until the entire dresser is stained. Once dry, you may repeat this process to get the color desired.
Step 5: Apply polyurethane finish.
Once your stain is completely dry (typically after 24 hours), apply a polyurethane finish to seal and protect your finish. Follow the manufacturer's directions; these vary according to brand. Allow your finish to dry completely.
Step 6: Affix hardware.
Replace the hardware when the polyurethane has dried completely.
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