In most martial arts schools and always in a TMA dojo, you will learn kata. Kata is a set of pre-arranged movements that incorporate strikes, blocks, kicks and other elements of your style. You can get overwhelmed when you first see a kata demonstrated at full-speed by your instructor or senior students. Others, like Sanchin, seem deceptively easy at first. I remember thinking about Sanchin, "Hey, you just walk slow, throw some strikes, rinse and repeat and you're done". That was wrong.
In Uechi schools, you will learn kata Sanchin first, and throughout your training. As you progress through the ranks, there will be new dimensions taught and self-discoveries for you. Most instructors will then teach you katas Kanshiwa and then Kanshu. They do look difficult, but as you focus and practice more it will all come together for you. What is the best way to learn a kata? Everyone has different methods to learn them. The following ones help me with learning my katas.
Keep a notebook. It's easy to forget the many things taught in class. Write in it after each training session. Anything that strikes you as useful, unusual or just 'cool'. Of course instruction and tips from your instructor should be recorded. With kata, breaking down the individual steps on paper can help you visualize it better when practicing it at home.
There are many kata videos on the Internet. I only recommend utilizing these as you progress in rank. There are some issues with them that can negatively impact your learning. The performer could be performing with poor technique or showing a version slightly different from what you are being taught. For example, there are plenty of Kanshiwa and Kanshu videos to watch. But none are exactly like what we learn in my school. If you are having trouble remembering your kata's movements, then only use these to help visualize the the order of the movements; and only if the performance's basic steps are just like your kata. This can be hard to determine as a beginner.
Practice. A lot. Then some more. Practicing will help you learn and perform the movements you have visualized or written down. Once you don't have to *think* about the movements, you can work on your technique. It can be difficult at home, but try to practice in a room with a mirror or two so you can watch your technique. In my room I have two mirrors on one wall and use the reflection in a TV at the opposite end of the room. Dojos will have lots of mirrors so use them as much as you can in class.
Don't be afraid to ask questions. About anything. If you don't understand or forgot how to turn in your kata or want to know how a strike or series of moves is applied (bunkai), just ask. You'll get an answer and each one will help build your knowledge of the kata.
Implement the feedback you receive from your instructor and senior students. In TMA they will earnestly help you. The senior students were at your level not too long ago and they remember the good advice and instruction given them by their senior students. I sure do.
Try these tips and see what works for you. If you have something not included, please comment and share. I hope some of this can help you learn your kata and be a better TMA practitioner.