It's been a while since I had to do this but it's certainly something you should be able to do. It should be a matter of loosening the rear wheel slightly and tightening or loosening the adjusters either side of the wheel. This is made much easier if the bike has a centrestand or paddock stand to get the wheel off the ground. Chains typically develope tightspots and the aim is to get the chain set with the chain at its tightest point when you move it up and down with a finger at the centre point between both sprockets. Sounds complicated but it's not really. In my day, no more than an inch of play should be allowed with the chain at it's tightest point.
If the chain has a huge amount of slack there is a danger it could jump either sprocket and the wheel to lock up - not good so it's best to check this out.
As I said, I have not done this for a while so check your manual - but wheels are still round and chains still oily!
Edit - Iggy got his reply in before I finished typing - glad I'm not far out though
