You can disable autoplay by unchecking "autoplay" in the right sidebar or in the player's settings menu. YouTube saves the setting in a cookie, so it will no longer play related videos automatically until you enable the feature again or clear YouTube cookies.
YouTube has a video and a help center article that offer more information about this feature:
"Once a video is over, you'll see a 10 second countdown that tells you what's going to play next. The next video that plays is determined by your viewing history. If you want more time before the next video starts, pause the countdown by scrolling down past the video player. You can also pause the countdown by typing, either a comment or something into the search box. Also, you can click 'Cancel' on the countdown screen to stop the next video from playing."