How do you hook up a 500k micro farad?

A capacitor of 0.5 Farad should have screw or spade terminals, with clear polarity markings. POLARITY IS EXTREMELY IMPORTANT!

The "-"/negative terminal needs to be connected to ground, while the +/positive is connected to the vehicle power. Reversing polarity will cause the capacitor to explode.

You will also want to charge the capacitor initially through a resistor to prevent blowing a fuse/breaker. A 100 ohm resistor will keep the current below roughly 100mA during charging. Let capacitor charge 15-20 minutes if it is a fully discharged capacitor. Once charged remove resistor and connect power cable directly to capacitor.

Once charged, large capacitors can dump large amounts of current, creating a fire hazard! Ensure all connections are well insulated once connected, and the power cable is sized to match the power of the component.