The art of using breadboard
Breadboarded circuits - both push-in and soldered can be made quite neatly if the components are sensibly laid out.



Figure 1. A large breadboard with neat layout and wiring. Source.



Figure 2. A simpler example from How to use a breadboard. 

I strongly recommend that you buy a jumper wire kit.



Figure 3. A jumper wire kit in colour-coded sizes, stripped and preformed. Image: Farnell.

I purchased a kit that used the resistor colour code for the short lead lengths. Jump 1 row was un-insulated, red = jump 2, orange = jump 3, yellow = 4, etc. This is really handy as you can count the rows and pick the correct jumper by colour so easily. A reel of solid-cored wire can be used to make custom lengths.