Start from a seated position, traditionally from 'Seiza' (正座), with your sword-cleaning kit opened on the floor in front of you.

Hold your sheathed sword with the convex part of the 'Saya' (鞘), scabbard, facing upwards, in your left hand, with your palm up, and the butt end of the 'Saya' pointing down and forward to your right. Your right hand holding the 'Tsuka' (柄), hilt, from below as well.

Slowly, and, in a single motion. Pull the blade carefully out of its scabbard, with the cutting edge still pointing upward. Making sure the 'Mune' (棟), back of the blade, keeps in contact with the scabbard, but without pressing it down.

Put the scabbard next to your left leg, with the opening facing to your rear, and the convex part of the scabbard facing your leg. Move the sword to your left hand, holding it with the edge pointing upward and to your right.

Take, either, a piece of clean sword-cleaning paper, or use unscented tissues as they keep clean in their boxes. With it remove any small pieces of wood from the scabbard using a brushing motion.

Next, with another piece of paper, remove the old oil from the blade by applying it at the base and fold it around the back / ridge. Then, with a single motion, wipe upward toward the point, with the paper, applying a little pressure. Do not move the paper back and forth please.

Reapply the paper at the base and wipe again. Make at least three unidirectional strokes in this way.

Holding the stick of the device in your right hand, lightly hit the blade with the ball shaped part, distributing the powder along the sides and the ridge of the blade.

Rather than covering the whole blade, apply the powder liberally in intervals along it.
The 'Uchiko' powder will absorb any remaining oil left on the blade.

Next, take a clean piece of sword-cleaning paper in your right hand and carefully wipe the powder off the blade, the same way you did with the old oil.

Carefully inspect the blade.

With a piece of clean cotton flannel, to which you've added a few drops of oil, apply the fresh oil evenly along all the surfaces of the blade, using a unidirectional stroke.
Make sure you do not apply a heavy coat of oil, as it might soil the inside of the scabbard and thus may attach unwanted dust etc. to the blade's surface.

Traditionally, 'Chōji' oil is used when cleaning a Japanese sword.

Put the sword back into you right hand and pick up the scabbard with your left, the convex part of it facing up. Gripping the 'Saya' with your palm up, carefully insert the point section of the blade into the scabbard's mouth, carefully resheathing the blade while resting the back of it against the scabbards inside.