Most private lessons are for one hour, once a week. That leaves 167 hours during the week where your practicing is not supervised by your teacher! So how do you make sure that you're practicing correctly, in the manner that your teacher suggests?
The fact is, it's simply impossible for you to remember everything that happens in a lesson. I require that my students bring in notebooks so that I can jot down important concepts for them, but so much in a lesson is shown visually, or demonstrated aurally with the instrument -- how do you remember those ideas?
The simple answer is recording. Recording your lesson allows you to review concepts when you have questions about them, and also serves as a great feedback tool: most students have never actually seen or heard their own playing! Seeing and hearing yourself will be a shock at first (I know from experience!) but it's the quickest path to improvement.
Audio or Video?
When it comes to recording, audio recording is great, video recording is even better. It used to be that audio recorders were significantly cheaper than video, but now both can be had inexpensively. And a high quality video or audio recorder isn't necessary, you just need something that gives you a good idea of what you look and sound like. Something like the Flip UltraHD Video Camera (about $140) or Olympus Digital Voice Recorder (about $30) is all you need. The Flip is especially handy because it can plug right into the USB port on your computer, so that you can easily save and organize your lessons.
After the Lesson
A good rule of thumb is to review the lesson the day of or the day after the lesson while the ideas from the lesson are still fresh. Often it's not necessary to listen to the whole lesson, just skip to the parts that you had questions about. Jot down concepts in your own words in your notebook, or write down questions that you have for your teacher to be answered at the next lesson.
Do you record your lessons? Do you have other tips for getting the most of your lesson?