Use a method called “water popping” in which you run a wet mop or cloth over the newly-sanded floor to raise the grain; this will cause the wood to better accept the stain. Allow approximately 30 minutes drying time before staining.
Dip rag or sponge into stain and apply stain to floor, going with the grain rather than against. Work from one side of the room to the other, frequently wringing out rag or sponge so coverage is even and stain doesn't pool on floor.
After 5 or 10 minutes, vigorously wipe to remove excess stain. The amount of time you allow stain to soak into wood will determine the darkness of the final product.
Following manufacturers' instructions, allow time for stain to fully dry then brush on a coat of polyurethane for a durable finish.