Chains will stretch over time so it's important to make sure it is at the correct tension. A chain that is too loose will wear fast, damage the sprockets and potentially dismount or break. A chain that is too tight will create a mechanical bottom out of the suspension and not allow full travel of the rear end. This will also stretch the chain causing tight spots and a potential break. Moral of the story is to run the right chain tension that is suggested by your OEM. Not all chains should be adjusted to 1.5" like many people suggest, only your owners manual will lead you the right way (except for us at TTRNO of course).
First step is to check the chain tension you currently have against what your required tension is. Using a set of calipers or a tape measure, measure the amount of play in the chain centered between the front and rear sprockets. It is also important to rotate the wheel and check chain tension at numerous spots, this will ensure there are no tight sections in the chain. If there are tight spots replace. As you can see from the photo, Ducati provides the chain tension specifications on the side of the swingarm.
If your tension is not correct, loosen the rear axle bolt so that the adjusters at the back of the swingarm can be moved back and forth. The axle doen't have to be too loose, just enough so that the axle will move back and forth in the swingarm.
Adjusting the position of the rear axle is what tightens and loosens the chain, so the axle carriers on either side of the swingarm will do all the movement you will need. By turning the rear bolt clockwise, the carrier bolt will thread into the swigarm, moving the axle forward and loosening the chain. Turn the bolts counter clockwise and the chain will tighten. Make sure to do all adjustments in small increments on both sides of the swingarm to ensure that the rear tire stays properly aligned. Each axle carrier has small lines engraved in them to easily tell when both carriers are in the same position. This process of adjusting each carrier to the same position and ensuring the tension is correct takes a bit of patience and attention to detail, but once all 3 components are correct your almost done.
Here's a little trick of the trade. Often times, when you tighten your axle, the clockwise motion will end up pulling the axle back and in turn tighten the chain again. The easiest way to avoid this is to put the bike on a rear stand, put an old screwdriver handle between the chain and sprocket and push the wheel forward. This additional tension on the chain will ensure that the torque applied from the wrench does not mess up all your hard work.
Using a properly calibrated torque wrench, tighten your rear axle to the torque specified by the manufacturer and RECHECK ALL OF YOUR WORK. Make sure your carriers are in the exact same spot and your chain is at the right tension.
Congratulations, you just tightened your chain!
If you would like to learn the best practices of cleaning and lubricating your chain visit "Basic Maintenance - Chain Clean and Lubrication" and if your chain has seen better days visit, "Basic Maintenance - Chain Replacement."