When you want to hide a screw in woodworking, you need to either use a series of drill bits to make first the plug hole, then the clearance hole for the screw to go easily through the first piece of wood, then the pilot hole for the threads to grip in the second piece of wood. Or you can use special combination bits that do all of that in one step.
Now the problem is how to get a plug that doesn't stand out. If you use standard purchased wood plugs or cut off pieces of dowel to make your own plugs, you will discover that when you apply a stain, the top of your plug is end grain that will absorb more stain that the face grain of the piece you are working with. You see this dark staining problem on both the left and right sides of the plug I have circled in the photo above. The circled one, although not perfect, actually has a chance to blend in. In fact, if I had done a more careful job of drilling the plug hole and of installing the plug, that ring around the plug would almost disappear. How do you do that?
You need to cut your own tapered plugs. You obtain a tapered plug cutter as in the last photo and cut plugs out of scrap pieces of the very same wood you are working on. That means that the colour and grain style will match. By being tapered, the more you drive it in, the more it closes up the joint on the top surface of the wood. If it bottoms out on the screw, shave a bit off the tip of the plug and try again. The more you work at choosing where to cut a plug so the grain will be similar to its final destination, and lining it up when putting it in the hole, the more you can make the plugs simply disappear.