MOSFET Common-Source Stage Confusion
The thing missing from that graph is a load line.

Let's say VDD is 6 V and RD is 15 k&ohm;. If the FET was a dead short (VGS = 0 V) then RD would draw 6 V / 15 k&ohm; = 400 &mu;A. If the FET is cut off then it draws no current though RD and VDS = 6 V. At all points between the resistor drops a voltage proportional to the current going through it.

So we draw a straight line from 0 V and 400 &mu;A to 6 V and 0 &mu;A. Wherever that line intersects a VDS curve is the current and voltage across the FET at that VGS value. For intermediate points you must extrapolate to get the approximate VGS value.