Whenever Sensei met with another martial arts teacher, they would lament about their students and every once in awhile they would talk about some student being, "Well trained." This always puzzled me because Sensei would comment that someone is well trained, but he never talked about the criteria for what it meant to be well trained. Only after I became a teacher did I realize what Sensei was talking about when he said that someone was, "Well trained." Generally speaking, being well trained means that one does the right thing at the right time with a sense of spontaneity and seamlessness. Sensei once told a story about a well trained a student who put a lit cigarette in between this famous sword teachers fingers just as he brought his fingers up to his lips. It was so spontaneous and fast that Sensei didn't even see the student light the cigarette.
Spontaneity and speed can only be achieved after the student has achieved ishin-denshin. Ishin-denshin refers to the connection between two people. The teacher's mind thinks it, the student's intuition perceives it.
How does the student develop intuition? Intuition is nothing more than a heightened sense of awareness that is only developed through experience. A good student reads all the clues then lets his intuition take over acting.
Training intuition in Aikido is no different. You have to do the techniques over and over ad nauseam before you can develop an intuition about what is coming next. Once you can do that then you try and take your training to the next level and spend time with the teacher trying to further develop this awareness and intuition. If one can successfully read the teacher and know what he wants before he wants it, you will have something truly special and there won't be anything you can't learn or eventually do.