I have heard something about cold storage. What is the best way to set up a cold storage for IOTA and why is it safer?
It depends on what you define as cold storage.
IOTA is stored on addresses in the Tangle. The Tangle is similar to Blockchain in that it's decentralized among all the users. Your Seed is merely a password to access the balances inside the addresses in the Tangle that you own.
Therefore, your Seed is what you are trying to store securely.
You have several options:
1) Paper wallet: Write your seed out on a piece of paper, or generate a QR code with your seed embedded into it. This is now your personal access code to your IOTAs with no one else having access to it unless they physically see it.
2) Digital Encrypted wallet: Put your seed into an encrypted password manager database, such as Keepass. Set your password and save the database file onto a USB drive. Your personal access code is now stored safely on your drive with no one else having access to it unless they physically obtain the drive and know your password.
3) Hardware wallet: these do not exist for IOTA yet -- but in the future, they will serve the same general purpose as option #2, but more streamlined.