There is no way to "be good at" yoga in the broader sense of the term because yoga is not just a way to exercise — in fact, mentally and spiritually experiencing universal oneness means you're doing yoga. That is why one of the things yoga teachers smile knowingly at most often is when students say, "I'm bad at this." Admittedly, where the body goes the mind tends to follow, so circling back to the physical aspect of it means getting on a mat is the ideal way to debunk the stellar-yogi myth.
Take your sweet time
Now that your perspective is flipped and ego spun around, take your time on that mat! Pay attention to your breathing, the instructor's cues, and any movement limits you may have in this moment. Moving slowly throughout yoga class has myriad benefits.
First, it allows you to intimately learn your mind-body-breath connection instead of hypothesizing it from a lecture or article. You may come to know aspects of how oxygen flows (or kinda doesn't) throughout you. Do you hold your breath more than you thought? Are there certain poses where your breath becomes hitched or ragged? Can you tell what body parts have a harder time fluidly moving breath through them?
Second, not rushing your yoga means you can really listen to the teacher. Are the instructions clear? Are you feeling any resistance to an authoritative voice or do you welcome some instructional clarity? Is your inner dialogue aligned with how the poses are detailed — aka are they saying to move mindfully but something about holding your leg up for that long pisses you off so you move quickly to avoid it and sabotage your last shred of confidence by suddenly realizing all the world's problems are surely your fault? Actively listening to your yoga teacher will help you develop the inner navigation system by which to hear and respond better to yourself as well.
Rounding out the number three benefit of a no-rush mindset on the mat is your own physical boundaries. Have an injury? Arrive early and notify your teacher so they can model modifications for you. Can't do a certain asana? Sit in Lotus and watch the teacher or fellow students demonstrate it safely. Heart rate going up and muscles giving out? Take as many Child's Poses as needed. Feeling dizzy? Assume Savasana and come back to your breathwork.
Ditch your "competitive sport" persona
Who's that girl you've become on the mat just 20 minutes in, staring at the yogini in front of you to meet or exceed her Chaturanga reps? Dudes, thrusting into Bridge pose with the same "ugghhhaaaaahhh" noise you make dropping weights at the gym is not what it's about. Your first yoga class is about enjoying a non-competitive experience and being non-judgmentally open to what "comes up" (more on that new-age lingo can be found in Ruby Warrington's Material Girl, Mystical World: The Now Age Guide to a High-Vibe Life).
While yoga will expand your views to the point that you wonder who you ever were before you "found your way back to yourself," it's not very yoga-like to compete with your teacher. Your teacher is (hopefully) well-trained and it takes years to practice yoga so much that the physical part of it becomes the least important part of it. Why do you need to do what he/she does today? When your practice deepens over time, won't those positions look different in your amazing, diverse body anyhow?
Focusing on "being good at it" detracts from your yoga empowerment
Attempting a few basic yoga poses at home and delving into the lineage's history is a great way to become move involved in your yoga practice, but I also think there's no comparison to a mental and spiritual up-leveling quite like not knowing what to expect and subsequently having parameters to define success (read: the illusion of success because again let's face it — it's yoga). Suddenly, you'll respond to situations off your mat with a resilience you never knew was in you, cut ties that no longer serve you, form friendships that truly nourish you, know your body like a chakra-crazed ninja, and oh, guess what? As mentioned, the body will follow. Yes, you will get stronger. Yes, you will become more flexible and agile. Yes, your shape may shift. Yes, your skin and hair and digestion and sexual energy will unlearn their current states, rest, and revive.
Enjoy beginning yoga; it is the beginning to the end of everything you thought you knew and an incredible way to connect with What Is.