Solve lots and lots of problems! Competition math is unique in that, for the most part, there really isn't a curriculum of things you need to understand per se (it's a lot more about the reasoning and critical thinking skills you develop over time), and all you need to know in terms of content can be found in the books I mention below. The best way to get a grasp on the kinds of questions that are asked in the AMC and to get better is to simply practice a lot! Like I mentioned earlier, check out the AMC 10 problem database (https://artofproblemsolving.com/wiki/index.php/AMC_10_Problems_and_Solutions) and the AMC 12 database (https://artofproblemsolving.com/wiki/index.php/AMC_12_Problems_and_Solutions), as well as these two resources: https://artofproblemsolving.com/wiki/index.php/Mock_AMC and https://ziml.areteem.org/ziml/practicecontests.php?p=MockAMC for practice problems. I also know that the MATHCOUNTS Trainer (at https://artofproblemsolving.com/mathcounts_trainer) and For the Win! (at https://artofproblemsolving.com/ftw) are amazing game-show-style ways to try your hand at some problems. These are geared more towards the MATHCOUNTS and AMC 10 in terms of difficulty level.
Read math books. If you're willing to invest in books, the absolute best books are the Art of Problem Solving book series: Art of Problem Solving Volume 1: The Basics and Art of Problem Solving Volume 2: and Beyond. You'll need to get the solution manuals as well. I would probably start with the first volume and work your way up to the second, but that depends on how confident you feel with competition math already! You could start at Volume 2 if you feel relatively confident with the competition math in middle school and on MATHCOUNTS (if that is something you've done) as that's mostly what Volume 1 covers. Another book I've found to be really helpful is the Three-Year MATHCOUNTS Marathon by Karen Ge. I know that this is geared towards the MATHCOUNTS competition, but the difficulty level of the problems in the book are way above middle school. All the concepts explored in the book are very relevant for varsity (and JV) competitions, which relate so well to the AMC, and you can get so much out of the concise explanations throughout the book. Also, this book focuses mainly on AIME problems than the AMC, so it is a bit further down the road from AMC, but A Gentle Introduction to the American Invitational Mathematics Exam by Scott A. Annin is also a fantastic resource. Feel free to ask in the comments if you want even more book recommendations!
Take an online course. If you're super invested in this, the Art of Problem Solving has a lot of online courses specifically tailored to the AMC and AIME series, including a Special AMC Seminar series that lasts for one weekend a few weeks before the AMC, where you're given a comprehensive crash course. There are also some free videos on the AoPS website that are helpful.
Attend other math competitions! This is pretty self-explanatory; finding all the competitions in your area and competing is the best way to practice for the AMC. If you live in Georgia, feel free to reach out because I can definitely discuss local opportunities with you.
Check out cheat sheets! One way I personally really like to study for math competitions is by finding "cheat sheets," essentially documents that compile formulas for you to learn. This is by no means something meant for you to memorize or for you to feel like you have to know entirely (because honestly, you can do really well on the AMC without using any formulas!). However, seeing lists of formulas and trying to figure out how they were derived and how they would be used helps you see the swath of potential concepts in math tournaments and learn how they all fit together. My favorite at the moment is Eashan Gandotra's Formulas for Pre-Olympiad Math, but I also like Coach Monk's High School Playbook and the outline All of Math in Three Pages. You can also check out Jim Sukha's ARML Handbook and Tom Davis's Contest Geometry Handbook. (All of those descriptions are linked, so click on them!) Again, these are not for you to memorize but to give you a reference sheet as you pick up concepts in contest math and to give you something to review before the AMC or any competition. It really helps me get in the mindset before taking a math competition to review one of these sheets, so that's something unique I've picked up over the years.