Do you have a masonry chimney? There should be a clean out on the bottom of the chimney. On a sunny day you should be able to see some light coming in at the top of the chimney. Use a mirror to look up. You can also try using a flash light with a mirror if you are in a hurry.
Warning!! Shut the Gas Off To Your Water Heater If Your Vent or Chimney is Blocked! The Fumes Can Be Dangerous!!
Can you clean your chimney yourself? Yes, but there is danger involved. You need to take safety precautions before you attempt this. It means getting up on the roof and running a special brush down the chimney. A set of rods and brushes will run between $20 and $50. Don't like being on the roof? A chimney service will run between $75 and $200. You have to do something if your chimney is clogged. For homes with a fireplace, regular chimney maintenance is a must.
You may have a double wall pipe that is used for the chimney. The fittings that lead up to it should be screwed in place. You can remove some of the fittings to get a look up the chimney. Same concept look for daylight or use a flashlight to check for obstructions. If the obstruction is within reach you can use something to clear it out. For an obstruction that is out of reach you will need to call a service.