The simplest (KISS) way I have always taught it is:
Draw a sloping front on a piece of paper. mark 'C' under the slope (for 'Cold') and 'H' above.
Cold air is more dense than hot - OK?
Now draw two vertical columns, one in the hot air and one in the cold air, passing into the hot (through the front).
You will replace the bottom of the hot column with colder, denser air as the front moves across. More mass of air in the column = more pressure.
Plenty of info on QNH/QFE etc via Google if you look or perhaps a met man with spare time will help.