Before going into how each become one, I'd like to point out here that I passed my OCT and AQI scores and had full intentions of going to OCS. But I found out you could get a reserve officer rank through correspondance and started working on that.
Unfortunately, the Army terminated the program about half way through it.
To go to West Point, you had to either be the son of an Officer who had already gone to West Point or you had to write to Senators and request an appointment.
West Point was considered -- and still is -- to be the ultimate way to go through the ranks and become a General Officer.
Its a bit harder to acheive the rank of General by going to ROTC, but it can be done. John N. Brandenburg, he was an ROTC trained officer and he retired as a three star General.
Both West Point and ROTC involve 4 years of college.
OCS is the way enlisted men become officers under normal military conditions. In times of combat, direct commissions can do the same. Many Warrant Officers jumped from Warrant Officer to Officer.
Supply and demand dictated policy and when the war was over, a lot of Officers went back to enlisted or Warrant -- or simply got out -- when they received reduction in force notifications.