If you don't have any more free slots in your Items screen, you are able to transfer items in your Items screen to your Storage, located in your apartment. To transfer an item to your Storage, click on the "Storage" button underneath the item's name. The item instantly goes to your storage.
Retrieving Items from Storage:
To take items out of your Storage, go to your apartment where you will find a drawer called Storage (indicated by arrows). Click on that and the Storage screen comes up. Select the "Take Out" icon and the Storage screen dissappears. The item has been placed in your Items section.