When a road bike is properly set up and maintained, it should be relatively free of squeaks, creaks and clicking noises. Most bike owners, however, will have to diagnose an unusual noise at some point. Fortunately, a clicking chain doesn't require the assistance of a pro mechanic. The clicking most likely means that your chain needs lubrication or your front derailleur requires a simple adjustment. Whether it is making noise or not, you should always check your drivetrain to ensure that it's shifting quietly and efficiently before you ride.
Check your chain. A dry chain can produce a clicking sound.
Examine the chain links, especially the inner links. If they are frozen, difficult to move or if the chain has rust on it, it needs to be lubricated.
Apply a drop of the lubricant of your choice to each link. Follow the instructions for the chain lubricant, as each is different, and be sure to wipe off any excess lubricant, which will pick up dirt and grime. Use an old shop towel and run the chain through several times.
Check the front derailleur if the bike is still making noise. The clicking sound is most likely caused by the chain rubbing against the cage of the front derailleur.
Note which gear you're in when the clicking starts. If you're in an extreme gear, meaning the chain is on the smallest front chainring and the largest rear cog or vice versa, then the angle of the chain might cause it to rub against the cage. This action is called "cross chaining" and should be avoided because it will put excess strain on your drivetrain.
Trim the front derailleur. Because the angle of the chain changes as you shift, it will rub against the derailleur cage in some gears, causing a clicking noise. Modern shifters come with the ability to "trim" the derailleur, which means that the shifter has some shifting leeway and can move the cage out slightly to prevent the chain from rubbing.
Shift the bike into the gear where the clicking occurs. Grasp the front shifter and push the lever as though you were going to shift the front derailleur again. You should hear a small click, but the gear has not changed. Examine the front derailleur and you will see that it has moved away from the rubbing chain. Each company's shifters have a different amount of trim. Play around to see where your shifter's additional trim is and until you figure out how to shift without your chain rubbing and clicking.