What carb components do I need to check?
The carbs on the Ninja are really simple things and should never need to be completely replaced. There are a few components which may wear out, though. The float valves are these little spring loaded aluminum parts with a little rubber nub at the end. There is a float attached to this valve that pushes it up and closes it when the float bowl has enough fuel. These little tiny parts cost about $25 each, so your best bet is to remove them, clean them, and re-install them if you think they are the source of the problem. Another problem Ninja carbs tend to have is that the rubber O-ring that seals up the float bowl will get dry and shrink, and suddenly you will find that it looks like gas is raining down from your carbs onto your starter.
The third fuel problem Ninja owners are likely to have is when the vacuum operated petcock fails. The vacuum petcock keeps fuel from flowing out of the tank unless the bike is drawing a vacuum. This keeps the bike from flooding itself when parked. The needle valves should also keep this from happening but don't always do their job.