Depending upon the fixture it could be simply removed and replaced or it could be a job for someone who is good with electrical wiring.

Can you see a model number for the fixture? Post it and I'll see if I can determine anything helpful.

And to be safe, leave it turned off.

Does it have a little silver 'can' somewhere near the connection for the bulb? If so, you have a model that uses a starter. They're pretty cheap, and easy to replace (they are usually a twist-and-pull). If not you may have a ballast; a bit harder to replace, but still do-able for the average person.

Guys at the hardware store will be able to help you out on either replacing it or replacing the whole fixture. Next spring. You know you won't do it during the winter while it's still working.

I agree with Warpy that a guys at the hardware store will be able to help or if you have knowledge about it then you can see if there is any loose connection and wiring is done properly. Many times the winter also creates problem as the connection become moist. If ypu want I know one firm which provide solution to kitchen related problem so you can check it here.