We learn about the poppet and what caused it to be discovered near the end of Act Two. Herrick and other officials of the court come to John's house, and immeidately start searching, asking if they keep any poppets in the house. Earlier that evening, Mary Warren had come home from court and given the poppet to Elizabeth, telling her that she had sewed it for her during the court's proceedings that day. Unfortunately for Elizabeth, there was a needle stuck in the belly of the poppet, which the courts took as proof of witchcraft. We can piece together the events as follows:
1. While Mary and Abby are in court that day, Abby notices that Mary is sewing a doll, and that she put the needle in the doll's belly at the end of the day.
2. Abby, who was unable to cast any negative light upon Elizabeth Proctor in court that day, comes up with a plan. That night at dinner, in front of the judges, she sticks a needle in her belly, falls to the ground in pain, screaming out that it is Elizabeth's "familiar spirit" that put the needle there, through means of a voodoo doll. She says that Elizabeth made a doll, and through witchcraft, is manipulating it to harm Abby.
3. The courts issue a warrant for Elizabeth's arrest, provided they can find proof of the voodoo doll theory. While this is going on, Mary goes home and gives Lize the doll.
4. The court officials show up and find the doll. Elizabeth denies the charges, and even Mary says that Abby saw her put the nedle in the doll herself.
I hope that clear things up a bit. I hope it helped!