Single sided swingarms are a beautiful thing, not only for their form but their amazing functionality.  One reason to love a single sided swingarm is the ease of chain adjustment.

Checking chain tension is as easy as measuring the amount of vertical movement of your chain using a set of calipers or tape measure.  Compare your findings with what your bike manufacturer requires and you know what direction you must go in.  The only other measurement you should take is the rear ride height measured from the center of the rear axle to one stationary point on the tail section (I will explain why later).

First step in adjusting tension is loosening the pinch bolts holding the wheel eccentric.

Using the special spanner wrench, grab the teeth of the wheel eccentric and spin clockwise to tighten the chain and counter clockwise to loosen it.

Torque rear eccentric pinch bolts to the spec specified by the motorcycle manufacturer and you're almost done.  Because the eccentric of the rear wheel acts like any cam, the rear ride height will change as chain tension does.  

In order to ensure the same ride you had before adjusting your chain, remeasure your rear ride height from the center of the rear axle to the same fixed point on your tail section.  Raise and lower the rear ride height adjuster accordingly to reset rear ride height to what it was before chain adjustment.  Most riders will not notice a difference one way or the other, but if you're putting your bike on the racetrack this is imperative.  

If it's time for a new chain visit, "Basic Maintenance - Chain Replacement," and to maintain the chain you have on there visit, "Basic Maintenance - Chain Clean and Lubrication."