Bypass capacitors or decoupling capacitors are added between each power and ground line to filter out noise from the power supply and make the entire circuit more stable. Here is an excellent video from EEVblog that explains bypass capacitors.
Be mindful that electrolytic capacitors are polarized, meaning they can only be connected one way in a circuit. The negative lead is generally marked on the capacitor with a bar or "-" symbol, connect this to Ground (or the more negative line). Do not mix up the polarity as this will heat up and destroy the capacitor in a few seconds. Ceramic capacitors have no polarity, they can be connected in any direction. The capacitance of both capacitors can be changed based on the power needs, as long they support a minimum of 16V voltage.
DC input 12V
2200 uF - 16V Electrolytic capacitor + pin: +12V DC
2200 uF - 16V Electrolytic capacitor - pin: Ground
0.1 uF - 50V Ceramic capacitor pin 1: +12V DC
0.1 uF - 50V Ceramic capacitor pin 2: Ground
DC step down output 7V
1000 uF - 16V Electrolytic capacitor + pin: DC step down Vo+ output
1000 uF - 16V Electrolytic capacitor - pin: Ground
0.1 uF - 50V Ceramic capacitor pin 1: DC step down Vo+ output
0.1 uF - 50V Ceramic capacitor pin 2: Ground
Arduino 5V
470 uF - 16V Electrolytic capacitor + pin: Arduino 5V
470 uF - 16V Electrolytic capacitor - pin: Ground
0.1 uF - 50V Ceramic capacitor pin 1: Arduino 5V
0.1 uF - 50V Ceramic capacitor pin 2: Ground
Arduino 3.3V
10 uF - 16V Electrolytic capacitor + pin: Arduino 3.3V
10 uF - 16V Electrolytic capacitor - pin: Ground
0.1 uF - 50V Ceramic capacitor pin 1: Arduino 3.3V
0.1 uF - 50V Ceramic capacitor pin 2: Ground