Keep a notebook in your riding bag and take notes at the end of each lesson, and keep a progress diary with all your riding goals. Discuss your goals with your trainer. Exercise! Exercise is free and you can do it every day 😉 Ask questions, watch other people riding, video your lessons whenever you can. Go to horse shows in your area and watch the riders - not just in the ring, but also watch them warm up and cool off. Take your notebook and write thigs down!
When you get home, think about and write a list of things your instructor told you and really think about how you can improve
Have a friend come video your lesson so you can see what your trainer is critiquing as he/she is teaching from the ground. Then, review the videos over and over again. It's so easy with smartphones these days. Don't ask your trainer to take the video, ask a friend, family, etc.
Make sure you ask any questions you might have, and also watching other lessons is very beneficial. Watching is one of my favorite ways to learn!
Listening to your instructor and practicing what you've learnt when your not having a lesson :)
Watch other lessons and other riders. You can learn a lot by observing
Pay attention to what your trainer says to you, and to the other people in your lessons, especially if they are a little more experienced than you!
Ask any questions you have, your instructor will notice how interested you are and hopefully teach you more in your lesson.
Listen to EVERYTHING your trainer says :)