Here is a photo of my first breadboarded arduino.
Instructions are here.
Anyway, once you’ve done this, you can basically solder everything together on a small bit of PCB.
Another option is to build one of these RBBB things shop.moderndevice.com/products/rbbb-kit
Keep in mind that really with an Open Source design philosophy, the Arduino itself is a platform for innovation and experimentation — go forth and solder!