There are several ways to obtain Capital City items:
1. Capital City items drop during normal gameplay. Every time you match 4+ items, you have a chance of getting one (even matching 4+ grasses has a chance of generating a Capital City item). You will also get Capital City items from treasure chests!
2. Your Capital City buildings themselves will sometimes give you a lower tier building (for example, you may receive an "Ore" (tier one industrial building) from a "Barrel" (tier two industrial building).
3. You can go to the in-game Store and purchase tier one and tier two Capital City buildings with diamonds.