Sand the bare poplar wood. Start with the coarse, 80-grit sandpaper to remove surface marks, then re-sand the entire surface with 120-grit paper, and finally 180-grit paper, which removes small scratches left behind by the previous papers.
Clean the poplar with a tack cloth--a piece of cheesecloth impregnated with sticky resins that pick up sanding dust. Turn the tack cloth over as you work to keep a clean area against the surface of the wood for the most complete dust removal.
Apply a coat of stain-blocking primer. Follow the manufacturer's directions for application guidelines and drying time. Allow the primer to dry thoroughly.
Sand the primer coat very lightly with 180-grit sandpaper. Wipe the surface clean of dust with a tack cloth, turning it as you work as described in Step 2.
Paint the primed surface with a quality latex or oil-based paint and a brush made for the type of paint you use. Once the first coat is completely dry, add a second coat if the primer shows through the first coat or if the first coat is uneven in appearance.