Apparition is taught to students in their sixth year by a Ministry instructor. It's not part of the regular Hogwarts curriculum, but is an extra class available to students who wish to prepare for the Apparition exam when they turn 17.
When Harry Potter apparated (alongside Dumbledore) for the first time, he was already near the end of 6th year and it wasn't his academic lesson.
This is incorrect. Harry Side-Along Apparates with Dumbledore twice at the start of the sixth book; from Privet Drive to wherever Horace Slughorn was hiding out and then from there to The Burrow.