How to get rid of annoying screen info on my Nikon DSLR when viewing photos?

According to page 124 of the manual (well worth reading, by the way) you can use the up and down arrows on the directional pad to cycle through the playback display information.

You use the 'info' button to cycle through

That "annoying screen info" is how you learn.

Lets say you are reviewing your photos and you have two of the same composition but one you like one better than the other. You could look at the "annoying screen info" and see what the difference in settings is between the two photos.

An example would be that in one photo a fast moving object, a person on a bicycle, is sharp in focus and its motion is stopped and in the other the cyclist is not sharp, it is blurry and the motion is not stopped.

Perhaps you like the one that shows a sense of motion so you look at the "annoying screen info" to see that the shutter speed is three stops different between the two photos. You can learn ( make a mental note ) to use a slower shutter speed, close to the one in the photo you like for object moving at a similar speed.

All of this is assumes you care enough to learn or even understand what makes the photo you like good and how to do it again. If you don't care then why are reading this stack exchange?

I know this is not an answer to your question. The tone of your question make me think you do not care and this "answer" is to point out that you should care.

Go to playback menu-> playback display options-> select none (image only) then ok. Its done. Now when you view images press up/down navigate button.

On my D200 I went to the playback menu then to display mode then deselected Data, Histogram, Highlight, RGB Histogram, and Focus Area. Now I don’t have to use the up/down arrow to get rid of photo information.