Detach the seat. Leave it attached to the seat post and remove it as a unit.
Remove the handlebars by loosening the bolt at the top of the handlebar stem, which is the elbow-shaped piece of metal that clamps to the handlebars. Remove the stem bolt from the bike, keeping in mind that the handlebars and stem should come out as a unit. Leave brake cables attached.
Tape handlebars to bicycle's top tube.
Use a thin crescent wrench to unscrew the pedals where they attach to the crank - where the inside of your foot sits on the pedal. The left pedal may be reverse-threaded; turn clockwise to unscrew.
Remove both wheels. Replace wheels with a block of wood where the axles were to keep the frame from being crushed during shipping.
Get a bike box. Most bike shops will give you one, or sell you one for a few dollars. Check the size printed on the side of the box, which should be at least as large as your bike.
Put pedals and seat in a bag. Tie or tape the bag to the bike's frame, next to where the handlebars are taped.
Lift the bike frame carefully into the box and center the bike. Next fit the wheels in the box, slipping one wheel on each side of the frame.
Seal your box with heavy-duty packing tape.