On a Free2Play Team Fortress 2 Account, all your items are untradable by default. To make most of them tradable you will have to upgrade your account.
To upgrade your account you will have to purchase something from the in-game store. We suggest upgrading by purchasing a Mann Co. Supply Crate Key as seen on the picture below:
Upgrading your Account will expand your backpack from 50 to 300 slots and make all your future weekly drops tradable.