There is a good introductory article on trailerlife.com
I have the system by TST (tsttruck.com). I have had good experience with it and am pleased. Not to say that other systems have anything wrong with them either.
The valve extenders that come with the MH will likely need to be replaced. Mine were cheap plastic and the monitors would not screw on correctly. I changes to a braided steel type and they work with the monitors.
Basically, you program the unit to know which sensor is on which wheel (some do it automatically, some you put the unique identifier for each sensor in and tell it what wheel). The unit sits on your dash. It communicates wirelessly with the sensors. Mine shows pressure and temperature and rotates continuously through the six tires. If the pressure changes on a tire, it jumps to that one's info. You set high and low limits for pressure and temperature (the manual gives you suggestions). If a tire goes outside those limits an alarm sounds (audible and visual). Also if the tire starts losing air fast the alarm will sound even before it reaches the low limit.
The safety and peace of mind of knowing what your tires are doing can't be over stated. You are right on to be thinking about it as a priority upgrade. I would not go on the kind of trip you are talking about without having a TPMS installed.