What's wrong with the flourescent light over my kitchen sink?

The bulb prongs are not making a solid connection with the brass tabs in the brackets. Make sure the power is off to the fixture. Remove the bulb. You will see two brass tabs in each bracket. Use a small screwdriver, tip of a knife and slightly bend the tabs towards the center. Replace the bulb.

Need a new starter ( small round thing)

Sounds like a short somewhere. If you put in a new bulb and it does the same thing, you can start with replacing the starter, or get a new fixture.

New bulb?

try a new bulb first and if that doesn't fix it then more than likely the balast is bad and the fixture needs replacing. They wear out all the time

Tighten the bulb

That ususally means your bulb is getting close to burning out. Yes, first try replacing the bulb.

It needs a new bulb or ballist. (Check that spelling).