On another thread, Mendel commented that he had spent 12k astral diamonds on something that ended up being junk as though this were a ruinous problem. 12k really isn't much if you know how to make astral diamonds in this game. But I thought, if a sharp forum poster like Mendel had missed that, then lots of other, less sharp denizens around here probably did, too. So I'll explain.
The main source of astral diamonds is the leadership profession. You initially get one profession slot, but get others as you level up. You get profession slots when your main level hits 10, 30, and 60, when some profession hits level 3, 10, and 20, when three professions reach level 20, when you make something with a 100% speed bonus, and when you make something of tier 3 quality. So eventually, you get nine slots. I'll come back to how to open them efficiently later.
Let's suppose now that you have nine profession slots and have maxed leadership. How do you get your astral diamonds? Let's assume conservatively that you only log in once per day. On that one time, you have three slots launch "Battle Elemental Cultists" for 2000 astral diamonds each, three slots launch "Destroy Enemy Camp" for 1600 diamonds each, and three launch something else, let's say "Protect Magical Goods Market" for 500 diamonds each. Recall that you cannot have more than three copies of the same profession task in process simultaneously, which is why we don't just use nine copies of "Battle Elemental Cultists". That gets you 12300 astral diamonds per day.
And very importantly, this is per character, not total across an entire account. If you have five characters, they each get 12,300 astral diamonds per day. Cryptic has always been more alt-friendly than a lot of other game studios. Your costs for many things (though importantly, not mounts if you buy one with zen) will have to be paid for each character, but your income also scales with your number of characters.
Above, we were estimating conservatively that you'd only log in once per day. If you can log in repeatedly at different hours of day, you can do "Destroy Enemy Camp" three times per two days and "Protect Magical Goods Market" twice per day, sometimes replacing it by "Capture Bandit Leader" (1500 astral diamonds). That gets you about 17,000 astral diamonds per day. And again, this is per character, not account wide. This is also just from crafting, so it ignores invocation, salvage, and anything that involves actually playing the game. That adds up pretty quickly.
As I said above, this is the main thing that causes astral diamonds to be created in the game. Daily quests and invocation are much smaller sources. If you're not doing leadership, you're not getting very many astral diamonds compared to the people who are. So don't ignore the crafting system, or only think about gear or consumables that your character uses directly, unless you're willing to spend real-life money to get what you want. (Not that there's anything wrong with that.)
Now, I assumed that you had opened all nine profession slots and maxed leadership. So how do you get there efficiently? You probably want to rank stuff up quickly, but you probably also want to get some good astral diamonds along the way.
Early on, just level up leadership as fast as you can. Do "Tactical Training" once you reach level 7, "War Games Training" at level 13, and "Train for the Protector's Tourney" at 21 if you know it's going to be several hours before you can do anything again, unless you've got enough good astral diamond producing things available to fill all of your profession slots.
Speaking of which, the first good astral diamond producing task is "Battle Undead" at level 10. That's 400 AD in 6 hours, and not rare. The next good one is "Collect Taxes" at level 12, good for 800 AD in 8 hours. It requires a district map, but starting at level 10, you get access to the rare task "Seek Out Maps", which gives you two district maps in six hours. So once you reach level 10, you want to grab "Seek Out Maps" when it pops for you, and "Battle Undead" to fill other slots.
At level 13, you get "Patrol the Mines", which gives you no AD, but does give you 120 profession experience in only 4 hours, as well as a mining claim. You also get the rare task, "Protect Diamond Shipment", which gives you 1600 AD in 14 hours, but uses up a mining claim. Do "Patrol the Mines" often enough to always have mining claims available to grab "Protect Diamond Shipment" when it pops for you. At level 17, you get "Deliver Metals", which uses three mining claims to give you 1200 AD in 10 hours. So don't worry about generating too many mining claims that you'll never have use for.
At level 16, you get "Fight off Spellplagued", which is good for 400 AD in 6 hours. That's the same as "Battle Undead", but this makes it possible to do both at once if you like. "Fight off Spellplagued" also gives 120 profession experience rather than 80.
It takes quite a while to get leadership to rank 25. But it doesn't take that long to get it to rank 16, by which point, you're making a lot of astral diamonds, even if not as much as you'll get at rank 25.
Now let's return to how to open all of those slots. The ones based on your level or a profession level are obvious. But you can probably get the slots for a 100% speed bonus or tier 3 crafting sooner than you think. For the speed bonus, pick an armor crafting profession (tailoring, leatherworking, mailsmithing, platesmithing), as that's where it's cheapest to buy the profession assets. Then buy four of the blue quality profession workers off the auction house; this probably costs you about 50k AD or so in total. Use all four together to create something random, and then you've unlocked the slot.
Tier 3 crafting is a little harder. For starters, you can't get a tier 3 crafting result until level 10. Additionally, the profession tools are much more expensive than the profession people. Still, shop around for which profession makes it cheapest to get some blue and purple assets. You can use the top tier tools (for producing items at profession level 14 or higher) for lower level production; you just need one of whichever tool corresponds to the what you're producing. Purple tools that are used for only one profession tend to be cheapest to buy. Also consider buying four blues and crafting them into a purple, as that's often cheaper due to the rates at which people get the profession assets from packs. Still, be ready to spend a few hundred thousand AD for the crafting tools.
But even here, there are two important points to remember, both as a result of profession assets never becoming bound to a character or account. First, you can profession assets once, pass them around among your characters, and unlock the extra slots for all of your characters at once, not just one. Second, once you're done opening slots, you can sell the assets back on the auction house and recoup about 90% of what you paid. So you might, for example, need 50k to buy the people to unlock the 100% speed boost slot, but you get 45k back when you sell them. It can take a while to save up the money to buy the tools, but you can speed this up greatly by spending $10 to get zen, selling this for 500K AD, buying the tools, opening the slots, selling the tools back, and then still having 450k AD for your money.
Finally, for any professions other than leadership and perhaps alchemy, green workers are cheap. Don't chain together 21 tasks at 18 hours each to train the tier 3 workers. That's a waste of time that could be spent leveling or producing AD. Rather, buy green workers off the auction house for about 1K each.