The recoil starter is something that requires little in the way of maintenance; but it's worth taking care of it, if it's not to fail just when you need it, i.e. when you start the saw. Let's take a look at it after the jump...
There are a couple of different types of recoil starter on the market, from the most basic setup through to slightly more complicated systems such as the Stihl ErgoStart™ - which really does make starting a chainsaw very easy.
The basic principle is that as you pull on the cord, a pulley turns which will cause a flywheel to turn. This is the really nifty bit - as the flywheel turns the engine will also go round, but it also generates a little bit of electricity to send to the spark plug. With the engine turning and drawing in fuel, and the spark plug generating a spark, everything is set to run.
But how does it engage the flywheel when you pull and then automatically disengage when the engine runs? The recoil starter uses a small pawl which is thrown out when you pull on the cord, but is pushed back by the flywheel when the engine turns. It's really very simple, and there's not a lot to go wrong.
The main thing is that eventually the starter cord will break as it wears through use - normally this is at one end (near the handle, or near the pulley) and you can often see the cord fraying at these points. It's a good idea to carry around a spare starter cord when you're out using the chainsaw.
Replacing the starter cord is not too difficult (if you've got the basic system) and the following video shows you how to replace the starter cord on a Stihl chainsaw.
Setting the tension is important - too much tension and you risk damaging the spring or other components, and you won't be able to achieve the full 'pull-length' as the cord will bind before it reaches it's maximum length; on the other hand, have the tension too loose and the handle will not retract properly.
Fortunately it's quite easy to check for the correct tension; after retensioning, hold the handle down against the starter housing - it should return to the upright position and stay there. If it doesn't fully return to the starting position then there's not enough tension in the spring. To check that it's not too tight, pull the handle out as far as you can, then (and this is where you need three hands), keep it at full stretch and try to turn the pulley - it should be possible to tighten it about a ¼ of a turn.
That's about it really. Just keep an eye on the cord wear, and carry and spare around if you're out doing tree work.