In a nutshell:
peace enforcement = get between the different factions and pro-actively stop them kicking chunks out of each other. This may include going after known bad guys, disarming factions and engaging factions within the laid out ROE.
peace keeping = maintaining a presence once the above has been concluded to stop violence starting up again. There is usually a shift in the ROE that = non intervention unless you are under direct fire from one group or other. You can of course stand to one side and watch group A chop up/crucify/burn to death group B. This usually occurs if peace enforcement has not been concluded effectively.
peace support operations = this is what happens when the various factions have stopped chopping each other up for a period of time sufficient to declare an end to hostilities. This would include rebuilding of schools, etc.
Its not simple at all in reality. Getting govts to provide personnel with the right ability to complete peace enforcement is very difficult. It is not really a high tech option (see US "efforts" in the Balkans). What you need are competant bods on the ground.