in the Parliment there the supporters of the King would be sat on the right hand side of the President and those who supported the revolution would be sat on his left.

Conservatives fit into the broad area that is the Right and liberals fit into the broad area that is the Left but it is important to remember that the labels are massive simplifications of a diverse number of positions.

Conservatism is the idea that traditional values are best, at the most simple level - religion, law and order, family values etc. It is hard to really define though as it has different meanings beyond that for every nation - the Conservative Party in the UK is royalist while I can't see the Republican Party in the US going for that There is a tendency for it to be very much pro-capitalism and free market as well.

Liberal is the belief in freedom and equal rights but the exact balance of where that lies can vary greatly, since true freedom includes the right to discriminate which can run agaisnt equal rights.

The thing to remember though is they are very crude labels and can mislead if you simply follow them without thought and that their meaning varies from country to country and over time as well. It is a mistake people too caught up in their own ideaology make to label everyone who holds positions they disagree with strongly as being on the other side of the spectrum (be it the Left or the Right) when in reality they might be on the same side of the spectrum.