Eighteen real half-cells, drawn at their true heights on one voltage scale. Pick any two and the gap between the rungs is the standard cell potential. The higher rung is always the cathode.
Every value on the ladder is written as a reduction, so you never flip a sign. You subtract. Take the cathode value and take away the anode value, and the answer is the voltage you would measure.
Anything high on the ladder is a strong oxidizing agent, because it wants electrons badly. Anything low is a strong reducing agent, because it parts with them easily. So a species can oxidize anything that sits below it.