I've pasted the FAQ below.
The short answer: solve all your book puzzles, and get the Ultimate Card Pack from the Ultimate Replicator.
You can get replicators in three ways:
You can find replicators in Card Packs. You can get the most replicators in Card Pack 4, because every copy of card Pack 4 contains the Ultimate Replicator, which is worth 10 replicators.
Every time you complete a Clue, you get a replicator card.
Solving Book Puzzles
Find the codes and solve the puzzles hidden in the books. Go to http://books.the39clues.com/books to enter the answers and get hints. When you solve all of the puzzles for a book, you will get a replicator card.