Once you place the base of your European District, you'll see three doors floating over the top, allowing you to place items into three locations. One is for the "European Neighborhood," which allows you to store 12 homes in the same process that you would unlock storage spaces in a regular neighborhood. That is, you'll be given two storage spaces for free, and must then fill out the rest of this block by asking two friends to come and help. You'll then collect building materials to unlock Block two and can continue the process until you've unlocked and filled all three blocks with homes.
As for the European Mall, this allows you to store up to 12 European businesses in the same way. Finally, the European Center allows for the storage of 12 themed European Community Buildings. Again, you'll receive two storage spaces in each sector for free, but must then unlock the rest with the help of friends and building materials.
All told, this accounts for the maximum storage space of 36 slots. Unfortunately, you may not have that many items already in your town that qualify to fit inside this European District, but I suppose that gives you plenty of incentive to actually build some! We'll make sure to let you know when additional Districts with different themes launch in CityVille, so keep checking back!
Will you build a European District in your city, or do you not own enough items to make it worthwhile? Sound off in the comments.