You want to make a Lazy Susan?
Here are some working tips.
To draw a large circle put a screw through a long stick or yard stick and drill a hole for a pencil. When you use this for drawing the circle, you also have defined the centre of the circle with the depression made by the screw pivot.
Find a bolt, 1/4 or 3/8 inches in diameter. Drill a hole this size through the centre of the base circle and halfway through the top circle. If you put the bolt through a piece of scrap and then put your cut out circle on this pivot you can spin this wooden circle to see it is a true circle.
One of the best ways to perfect this circle is to lie a belt sander on it's side and spin the circle into the moving paper. It will remove wood until you have a perfect round. You can even do this with a block of sandpaper, but it requires a lot more elbow grease.
Now screw the Lazy Susan bearing into the base piece, being careful to centre it over the bolt hole. You can check how well you have installed this by turning it over, set the bearing plate on a table and spinning, checking if the edge stays in the same place all the way around.
Now turn the bearing so that the two plates do not line up. Then make a pencil mark in the base circle directly below one of the screw holes for the top part of the bearing. Drill a hole through the base piece large enough to run your screwdriver through.
Put your bolt through the base circle and into the socket in the back of the top circle. This will line the two pieces up together.
Spin the base circle a bit until you can see the screw hole in the bearing plate through the screw driver hole. You can screw in all four screws this way.
What makes the difference between a durable Lazy Susan and a cheap one? A cheap one has ball bearings in a plastic ring riding directly on the wood. This will not turn for long, nor hold up to much weight. You can identify the difference by looking at the bottom. If there is only one screw in the centre, you have a bearing ring riding on wood and the screw is the pivot. If you have no screws in the bottom but an off-set hole, you have a metal bearing plate that will last. These good bearings aren't that expensive, ranging from 1 to 10 dollars each, made by Canadian Bearings.