You hate it when you run into people who don't know crap about the class they're playing. Those players look like idiots, especially when they have nice gear, and what's worse, the people they try to play with treat them like idiots. *Instant kick you shitty nub.* Well, some people do their best to learn, but you really can't expect much with the current tutorial structure.
So the basic idea has been, more in-game help and tutorials. Yeah that's cool, but here's some advice on implementing it. First, there needs to be a hub for all this betterment, and the only obvious place for that is the class guilds, the way it's intended to be. These guilds need more love! As it is now, battle classes typically don't need to step foot in their guilds unless it's quest related, and those quests do little for making you better at your class. These are some of the things that would make guilds across Eorzea much better:
Directing players to their respective guilds - Every guild only exists in one city, so you won't be seeing the Gladiator icon in Limsa Lominsa or Gridania. Well, put a guild icon for every single guild in every single city, and if it doesn't lead to the guild itself, have it lead to an NPC ready to tell you everything awesome about your guild and why you need to go visit it.
Books - Every guild needs a bookshelf, and every bookshelf needs a wealth of information that is easy to access and useful. Keyword there, useful. Teach us about stats, tactics, abilities, combos, enmity, the elements. Unless it's meant to be a secret, put it on the bookshelf.
Interactive quests - This is where things get legit. New players don't need to kill things, they'll have the rest of their adventuring lives for that. Class quests should have interesting objectives that teach skill and tactics. Gladiator example: "Use your enmity abilities on this invincible mob to steal hate away from your NPC party members." Conjurer example: "This mob is wailing on you, and you're nearly out of MP. Sleep the mob, recover MP to full, and proceed to kill it with fire." Keep these quests imaginative and useful and the players will thank you for it.
Demonstrative NPC animations - Square Enix went through a lot of trouble to have random NPCs doing random shit in their guilds. Well, maybe they can make those animations a little more useful. Create looping animations of NPCs fighting each other. Gladiator example: Gladiator A and B are fighting. Gladiator B readies a weaponskill, Gladiator A uses Sentinel, Gladiator A takes minimal damage. Pugilist example: Pugilist A and B are fighting. Pugilist A uses Featherfoot, Pugilist B attacks and misses, Pugilist A flattens him with a weaponskill. These animations repeat endlessly, and show useful information like counters, as opposed to "how to drop your cesti."
Incentives - Gear and achievements for being a good player and learning your class. They're new players, throw them a bone and save the brutal in-game economy for later.
These are just some things that I think would improve the new player experience, and make them better players in the long run. Like this post if you agree, and throw your 2-cents into the discussion.