Which is important but only about 30% of the answer.
Your high level steps are as follows:
-detect where the user has clicked on your plane
-determine the position in the texture from the click location
-modify the texture (using something like ImagePainter or more likely just use ImageRaster)
-make sure the texture is updated (I think that's just one call)
The first two are where most of the work is, I guess. And that can be a pretty deep hole.
Edit: I've made quite a few assumptions from your question... such as what you mean by "display an image on the screen". You may want to provide more detail about what you are doing, what you've tried, etc.. Else treat my answer very generally.