Step-by-step explanation:
I assume you have constructed a circle using a compass with a certain radius. Keep the compass open at that dimension all during the process.
Your next step is to pick a point on the circumference. We will call it point A.
From point A as the center, you draw a small arc with your compass which will cross the circumference in point B. From B you do the same thing to get point C and so on until you get back to point A.
Now you connect A to B, then B to C, and so on.
You have built your regular hexagon.
Note that you can move clockwise or counterclockwise. It does not matter, you will have the same hexagon whichever way you go.
I hope this helps