Actually, Huck gets the ball rolling when he says that Tom's suggestion of holding hands and swearing to silence isn't enough. Huck says it's girlish to do it that way and only good for ordinary secrets. He suggests they use writing and blood.
Ever one to seize on an exciting idea, Tom is enthusiastic. Tom writes the following oath:
Huck Finn and Tom Sawyer swears they will keep mum about This and They wish They may Drop down dead in Their Tracks if They ever Tell and Rot.
Then, Tom takes out his sewing needle and has each of them prick his finger multiple times to get enough blood to form signatures. He shows Huck how to make an H and and F for his signature.
When Huck asks if this means they will never tell, Tom says yes, that this will force them to keep "mum" about what happened. He says they will drop dead if they ever break the oath.