After selecting 'New Game' there will be a list of options, with 'Apply Preorder Bonus' at the top. This will activate the DLC for that playthrough. This option also appears when you start a chapter out of Chapter Select.
The DLC will unlock the Crafting skill tree and the first Pistol ammo capacity upgrade.
The Crafting skill tree can first be accessed when you first play as Ellie in 'Waking Up'. After getting the backpack, press the touch pad button to open your backpack, press R1 to go to the Player Upgrades tab, then press the right directional button to access the Crafting skill tree.
The Pistol ammo capacity upgrade can first be seen in the chapter Patrol when Ellie can first wield the Pistol. The Pistol will have a 10 round capacity rather than the default 6 rounds, and will have a visually larger magazine.
The Preorder item can only be redeemed prior to a gameplay session starting. If a player has already started progressing through the game, and only then redeems the voucher, they would have to start a new game if they want to have those items unlocked.