The different phases are merely implemented at different times with the same rules applied to each phase (except the 4th phase which I'll explain in a while). When the MCO was first announced, it was scheduled to run for two weeks. Before that two week period ended, it was extended for another two weeks (the 2nd phase), and before that ended it was extended for a 3rd phase, and now the 4th phase has just begun.
The rules throughout the MCO were basically things like all non-essential businesses were closed, restaurants were allowed to operate but only for takeaway and delivery, all schools and universities and colleges were closed, only one person from each household was allowed to go shopping for essentials, all religious activities in mosques, temples, and churches were cancelled, so on and so forth.
Throughout the MCO if a high number of cases were detected in a particular area, it would be placed under an Enhanced Movement Control Order (EMCO). If you were in an area that was under the EMCO you were not allowed to leave your house at all for any reason, and nobody from outside the EMCO area would be allowed in. Supplies and food would be delivered door to door, and healthcare workers would setup a station inside the EMCO to screen everybody for COVID-19.
Malaysians were generally quite aware of the risks of the pandemic. This isn't the first infectious outbreak we've dealt with. Even before the MCO was announced many Malaysians were staying away from crowds, wearing masks in public etc. We did have a few who didn't abide by the MCO rules, but in general the whole country played its part, which is why we can see the number of cases decreasing.
In the 4th phase some rules have been loosened. Before this we were only allowed to travel within a 10km radius from our homes, but now that restriction is uplifted (within reason). Interstate travel was banned in the first three phases, but now people can travel from state to state after requesting for a permit. Students who were previously stuck on campus will be allowed to return home under strict supervision. Some business sectors will be allowed to open gradually, but schools will still be closed. I'll link a few articles below if you want to read further.