Empty your backpack. Remove all of your important papers, clothes, jewelry and accessories. Remove any garbage or lint as well.
Fill the bowl with hot water (but not so hot that you scald your skin when you touch it). Dip your washcloth in the bowl and gently rub the water over first the exterior of the backpack, then the interior. This will remove any dust or dirt.
Use the same damp washcloth and squirt a dime-size amount of dishwashing soap on it. This type of soap will remove grease and set-in dirt. Rub the washcloth over the backpack, first on the outside and then on the inside. Scrub roughly so a soap film appears.
Dip your second washcloth into the bowl of hot water. Rub the cloth on your backpack to remove the soap. Remember to wring out your washcloth frequently and dip it back into the water. Remove all the excess soap.
Place the backpack in your washing machine. Do not add any other clothes to this load. Most washing machines have at least three cycles: regular, delicate and permanent press. Choose the most delicate setting you have. Use hot water and a regular amount of laundry detergent.
Hang your backpack to dry. Machine dryers may damage the material, or it may catch on something inside the dryer. Air-drying is the safest method for keeping your backpack clean and new-looking.