The axle of the motorcycle has a nut on one side. There are also adjusters built into each side of the swingarm. Currently the chain has too much slack so I will loosen the axle nut and adjust the tensioners to take the slack out.
When I loosen the nut the wheel won't move because the tensioners are in place.
With the axle nut loose I can loosen the locking nut on the tensioner. It's the nut that touches the swingarm.
Next I will turn the adjusting nut on the tensioner to remove slack from the chain. Always adjust the chain side first!
If you do not have a caliper to measure the wheel's position in the swingarm you should adjust the chain side one quarter turn and then adjust the non-chain side one quarter turn. Keep going back and forth in this manner to ensure the wheel stays aligned.
The chain should have 30-35mm of movement. Make adjustments to the tensioners and then check the movement of the chain up and down. Keep adjusting until it is correct. It's important that you don't overtighten the chain.
When you finish you can tighten the lock nuts according to your manufacturers specifications. My bike says 10Nm. THen tighten the axle nut according to specs. For me this was 100Nm.
Now take the bike for a slow ride and see how it feels. If it seems right you can go faster. Then return to the shop and check the tension on the chain again. If it's still good you are done.