Sayyidatuna Aaisha [Radhiallahu anha] reports that Rasulullah [Sallallaahu Alayhi Wasallam] used to pour the oil on his left palm and using his right hand, he would first apply some oil on his eyebrows,then his eyes and thereafter on his head (the right side first). (Muntahas-sool vol.1 pg.320)

However, men should not waste excessive time and effort in grooming their hair, this was prohibited by Rasulullah [Sallallaahu Alayhi Wasallam] (Shamaail Tirmidhi Hadith35, 36) for it is a habit of women to do so.