Hearthstone 101: How To Get Gold Without Winning in Play Mode

The primary way of earning gold in Hearthstone is through completing "quests": these are in-game tasks, most of which involve winning with a certain hero or heroes to complete, and almost all of which require you to play against people instead of AI.
You get a new quest every day, even if you don't log in (but with a cap of three), and you can reroll one quest each day (this requires logging in, of course).

New players might find it difficult to complete quests with their collection of only Basic cards when they have to compete with players with better card collections.
To (somewhat) remedy that, there are also quests that don't require you to win to complete.  Additionally, I've created a Basic-only deck for each of these quests to help new players complete them quickly.

Basic Hunter deck for Beat Down
Basic Mage deck for Destroy Them All
Basic Druid deck for Only the Mighty
Basic Rogue deck for Spell Master
Basic Warlock deck for The Meek Shall Inherit

If you're a new player with just a Basic collection struggling to win in Play Mode, consider rolling for the quests above and try those decks too!

P.S. Each week there's also a Tavern Brawl (in PDT it's from roughly 10am on Wednesday to midnight on Sunday) in Hearthstone: basically a mode where things get EXTRA CRAZY.  (AKA much RNG.)
Your first win in Tavern Brawl each week nets you a Classic Pack!
Sometimes for these Tavern Brawls you play with a premade deck instead of your own; since you can complete quests in Brawls as well, the Brawls with premade decks in particular are helpful to players with minimal card collections, allowing you to compete more easily with other players and complete those win-requiring quests.
(Caveat: You need a class at level 20 to participate in Tavern Brawls.)

P.P.S. There's actually another quest that doesn't require you to win IN PLAY MODE.  The quest is Total Dominance, and to complete it you need to win 7 games, but you can play in Practice Mode and the quest is worth 100 gold!  It's awesome.

P.P.P.S.  There's one more quest that doesn't require you to win in Play Mode...it requires one of your friends to win!  Also, you get a Classic pack (worth 100g!) instead of gold.  The quest is Watch and Learn!  All you need to do is spectate a friend, watch them play a game and win it.  (You don't even have to watch from the start, all you need is to see them win!)