[John Chapman (OP)]

I understand the fundamental principle that haemoglobin has an affinity for oxygen which it binds to in the oxygen rich environment of the lung’s (the pulmonary) capillaries. But how does it know where the oxygen is needed and what makes it release the oxygen? And how is the CO2 transported away? Is CO2 also bound to haemoglobin and, if so, why does every schoolboy know that haemoglobin carries oxygen but never heard of it carrying CO2? And then how is the CO2 released to enable the binding of more oxygen?

In other words, we know that haemoglobin is the transporter, but what is the controlling mechanism?

[Bored chemist]

It's probably easier to answer the second question first. The CO2 is largely just dissolved in the blood. CO2 is a lot more soluble in water than oxygen is. Also some of it is acrried as thebicarbonate ion HCO3- because blood is generally slightly alkaline..
The heamoglobin storyu is a bit more complex. The simple answer is that it doesn't "know" when to give up the oxygen. The heamoglobin binds more oxygen where ther is more available to bind (ie in the lungs) and loses it again when there is less (eg near the muscles or brain.
However the detail of the amount of oxygen trapped vs the concentration of O2 is more complicated that you would get for a simple complex.
There's a whole lot of stuff about it here.
http://en.wikipedia.org/wiki/Oxygen-haemoglobin_dissociation_curve