How do I put the Safari Icon back on my desktop?

Is the Safari icon present in your Dock?

If you can see it there while running Safari but it disappears from the Dock after quitting Safari, simply drag it away from the Dock, and without releasing the mouse or trackpad button, drag it back to the Dock, in the position you would like it to be. It will remain there after quitting Safari.

If you prefer to actually have a Safari icon on your Desktop, click the Safari icon in the Dock and hold it until you see the contextual menu appear. Select Options > Show in Finder as in the following:

Then, drag it to the place on the Desktop where you would like it to remain:

You can then close the Finder window that previously opened.

Do not move the Safari icon off the Dock to the Desktop. Safari will not launch if you do that.