Summarize:

Wood fillers are thick pastes that usually come in round tubs. Use a small putty knife to apply the filler into the depressions created by your screw heads, as well as any knots or imperfections in the wood. Scrape away the excess filler, as this will make sanding easier later. Follow the product's instructions for application and drying times. You can leave the screw heads exposed if you like, especially if you may want to remove the ladder-stairs later. Use a piece of fine-grit (150-180 grit) sandpaper or an equivalent sanding block. Rub the entire wood surface with light and even pressure. Keep sanding until the wood feels smooth to the touch. If you've applied wood filler, wait until it's completely dry before sanding it. You may need to sand a bit more aggressively to smooth out excess filler. For your safety, wear a dust mask and eye protection when sanding. If you're painting the wood, apply a primer first and then 1-2 coats of your chosen paint. If you're staining the wood, apply a small amount in an inconspicuous area first to check the color. Then use a brush or rag to apply the stain, and wipe away the excess with a cloth. If you want the structure to retain a natural look, it's still advisable to apply a clear wood sealant, using the same techniques as you do for staining.
Apply wood filler to cover the depressed screw heads (optional). Lightly sand the entire ladder-stairs structure. Stain or paint the ladder-stairs to match the bunk set.