Chris has kindly pointed you to the links, but the answer to your first question (in a few words) is that the capital cost of paying for the new boiler gets added onto your energy bill per quarter. However, since the new efficient boiler will use less energy than the old one, the new quarterly energy payment you make will be less than before because the saving in energy usage is greater than the 'mortage' repayment for the new boiler. This is why the schemes have to be subject to an audit beforehand - to check that the old boiler is inefficient enough so the new scheme will save the householder money.
However, if you can get a new boiler for free (or subsidised) due to your age, that would be a better bet.