I will not consider myself to be an expert at arena until I can average 7 wins per match, but I play enough to offer some tips to help you get better:
1). Use a site like HSReplay to identity the best performing classes in the current arena environment.
Right now, the best classes are Hunter, Paladin, Warlock, Druid, Rogue, and Mage.
Don’t be afraid to lean into playing a class that is more your play-style rather than some other class that is performing better according to the stats, but you dislike that class and have a hard time making it work. For instance, I hate Demon Hunter, and I would rather pick Mage (with mediocre stats) over DH (when it has good stats). Right now, Druid is outperforming Mage, but I would pick Mage over Druid, because I have a lot more experience with playing Mage and making the class work for me.
https://hsreplay.net/
HSReplay can also help identify the best cards in the format for each class by looking at their win percentages.
I play on a mobile, but if you are playing on a PC there are add-ons, which provide scores to help you identify the stronger cards. Just be aware that things like card synergies or antagonisms, or mana curve can be factors, which override high scores for better draft choices.
2). Learn a little from watching an expert streamer who does a good job of explaining their decisions. Kolst does a good job at this, but his last YouTube post was like four weeks ago, and since then, the Meta has shifted away from DK, Shaman, and DH.
https://youtu.be/YFFSY7b_D3g?si=SWFKFZlE_yP0aqPZ
3). There are a lot cards in arena that are too broken or impactful for the format, which means that you must have quick answers to these cards or the board-states that they create, so I prioritize cards like removal, Rush, and Charge, because they can quickly impact the board to solve a problem. Cards like Oragami Frog or Burrow Buster are Rush cards that are often easy to draft.
4). As you draft cards be mindful of how the deck is going to win. This often means paying attention to card synergies. For instance, as a Hunter, based on what is being offered, are you going to lean into Beasts, Deathrattles, or Secrets? As Mage, one of your best win conditions might be to play Grand Finale to create a wide board of 8/8 elementals, but to do that you are going need a supply of cheap elementals.
One cannot just focus on drafting value cards or card advantage. As one drafts, it’s important to gather answers while identifying and developing a deck with win conditions.
5). Play on all three servers to get more quests and gold to fund your arena drafts while you are learning.