Gear shifting problems on second hand Boardman XC Team

Having bought this Boardman XC Team bike second hand I realised it was a bit rough. Halfords confirmed it needed lots of work (and new parts), but it would be worthwhile to do so. Well, it cost me £180 to do all the work, including replacing most of the gearing, but I am finding it difficult to change down on the back cog. I understand that this is a 'tap' system and a tap down seems to select a higher gear, but a tap to the left sometimes changes down, but often changes up. This is a real problem when climbing.
I am not very practical and would be interested to hear, a) what is the best way of shifting on this bike and b) If it needs Halfords to look at again, does anyone know when this might be possible?
Peter