Best thing to do is to pop down to your local bicycle shoppe and ask them for an old bike box,they usually have a few.
Next,strip the bike down so the bars/forks/wheels and pedals are removed[with the bars just leave the cables attached and wrap it inside the front triangle]
Put everything in said box-If theres still room at one end bring out the stanley knife[ask an adult if unsure better still someone sensible
]
cut the box so you can push one end closer and a roll of sticky later you have a smaller box.
Pack and voids with foam,bubblewrap,newspaper or anything else you can think of to brace it and stop the box from collapsing if handled roughly
[I find rolled up lengths of cardboard placed at right angles to the bike and sticky'd in the best way to support it]
Seal it up,address it and take it to the postoffice to be weighed[you dont have to say your actually going to send it with them but only getting a weight/cheapest PO price bu8t dont tell them that till theyve weighed it
]
Info on weight and dimensions in hand its time to phone around to get the best price,or online price checker on the couriers website.So much easier.
Where sending,get the company's[PO,whatever] fragile stickers put on,dont just write fragile-Thats an invite to the human mind