New Hearthstone players receive a lot of gold due to the easier achievements. One might feel inclined to spend this right away, and hope to get lucky. However, I suggest taking another path. Buying card packs is not the most efficient way to grow your collection. Doing well in the arena is much more beneficial, and achieving a 12 win streak could grant several packs, in addition to dust and gold. Though this way does require a bit more skill and knowledge about the game in order to be effective. Knowing which cards to pick during the drafting phase is crucial for succeeding in arena. Therefore, I would recommend saving your gold until reaching an adequate understanding of the game. In the meantime, complete the quests and achievements (don’t forget to re-roll 40 gold quests for a chance at a better one), play with the free cards, and study experienced players at youtube.com or twitch.tv. When you feel ready to start competing in the arena, start out by using one of the arena card tier lists that are available online. Oftentimes, card value outweighs synergy and mana curve when starting out, at least to a certain extent. As you get more experience, you will be able to incorporate these aspects as well.
If you have already been playing the game for a while, or just ran out of gold to use for new arena runs, it can be a tedious task to grind enough casual/ranked wins. But there are ways of making the process a bit faster. If you are able to resist the instant gratification of completing every daily quest right away, you can click on the “x” on a quest to re-roll it. This can be done once every day, and will give you a new random quest, and since there are different rewards (40, 60 and 100 gold), I only recommend discarding the 40 gold ones while completing the others.
The second way of improving the speed at which you acquire gold, is shortening the length of each match. Decks are built to gain advantage at different points of the game. What I suggest is using some form of rush deck, which aim to swarm the board with cheap cards and win as quick as possible. For example, control-warrior would be a bad choice for this purpose. Right now in the current meta, zoo-warlock is a cheap deck which is great for grinding gold. There are several versions of it online, or you can create your own and test it until you’re satisfied. The basic idea behind it, is using the hero ability of warlock in order to play as many cheap minions as possible in the early stages of a match. However, the meta is constantly changing, and this deck might be outdated in just a few weeks. But you can use the principles that are described above to adjust and adapt to these changes.
If you want to know more about hearthstone tips and strategies:
HearthPwn (forums and decks)
Hearthstone Mastery (affiliate link) Guide to both arena and ranked play