Is there a good way to farm crowns for beginners?
Farming
It is probably a good idea to speedrun everything until you get to the Snarbolax. If you care for it, any gear that you get from trading Snarbolax boss tokens, e.g. BTB or BTS, is decent and will save you some orbs. After you get whatever you want from the Snarbolax, move on as fast as possible. The idea is to get ahead asap to get to the best farming areas. Do everything on elite, as there really isn't any reason not to. If you find yourself lacking of skill, stop and practice a while. Don't waste your sparks, just go back to haven after dying a second time. Once you reach the 3* hall of heroes, you would probably want to farm "The Sovereign Slime", again on elite, until you get decent 3* gear. You can use the crowns you get for orbs from the Supply Depot on the tab on the right. By "decent", I'm talking effective gear such as Wolver/Gunslinger/Demo/Magic line gear, Brandishes/Final Flourish or BTB/Alchemers/Vaporizer bombs, and Plate(craft to Volcanic)/Owlite/Barbarous/Swiftstrike shields. This is just a recommendation, but it'll save a lot of trouble. the Arcade on elite has a higher orb drop rate, so that may be a good idea if you feel lucky. Arenas and Danger Rooms are excellent for this. After that, speedrun again and grind "Built to Destroy!" for 4* gear. Once again, the Arcade gives better orb chances but takes a bit more time. Boss tokens can be traded in for gear, which can be sold for crowns. Be patient and never buy stuff from the supply depot.
TL;DR: Boss missions will steadily give more crowns, while the Arcade has a bigger orb drop rate, especially Arenas and Danger Rooms if you are willing.
Correct me if I said something wrong ^_^
Even stratums.
Bosses happen to fulfill this criteria, but are not required.
My farming "The Gauntlet" beats most other's farming of FSC.
Thanks! If you'll excuse me, I'm off to grind for 5 hours straight. :P
Skepticraven gave you data on Arcade gates. The guild Lancer Knightz has detailed data on the crown payouts of missions. Those are the two kinds of information you need.
One more question: How do you get simple orbs of alchemy?
Read the wiki page Rarity, to learn about rarities such as orbs of alchemy.
The default way to get them is to save crowns, use those crowns to buy energy, and use that energy to buy orbs from the Supply Depot. However, you can also find orbs in the dungeon sometimes. They drop from treasure boxes on a particular stratum (see the wiki page). So you want to find places on that stratum that have many treasure boxes, such as arenas and danger rooms. But do not count on this method for getting orbs. Instead, recognize that sometimes you will have to buy them with energy.
I would find many people who are lazy, so waht they do is that they will take a 5* friend, and than just sit as they kill those monsters, and than take the money. Even if you are like squire rank, and your friend invited you to vana, you could play the support role. Many parties appreciate supportrole, and that is what I would do when my friend invitedme to vana, because I couldn't kill any monsters.
I would find many people who are lazy, so waht they do is that they will take a 5* friend, and than just sit as they kill those monsters, and than take the money. Even if you are like squire rank, and your friend invited you to vana, you could play the support role. Many parties appreciate supportrole, and that is what I would do when my friend invitedme to vana, because I couldn't kill any monsters.
By 'Beginner' I assume you mean a Recruit or a Squire...
Other than doing the Rank missions, just running the Arcade as far as you care to each day will help increase your crown income. The higher the difficulty setting, the more crowns drop per level. The levels that are Arenas generally drop more for the time they take to do (with the higher danger as well).
In general, crowns are needed and help ... but you also will need tons of minerals and you only get 1-4 per instance done. You will need these to make food for you Battle Sprite, so don't forget to harvest one each time.
Once you are a Squire, you can start dong the 'dailies' or Prestige missions, they are two levels and pay around 800 crowns at 'Normal' setting.
I would also strongly advise leveling your armor and gun/sword so you get more hp per click. That makes doing the instances at higher difficulty levels quite a bit easier.
Expect to make about 1000 cr for levels 1-3 and 2700 for 1-9 set normal.
The game is one of patience and learning the various attack moves of the enemies. Doing different types of instances will help make this process less monotonous.
That being said, some will say to Team with a higher ranked player and run the higher tiers. That is the 'easy way' for those who don't want to hone their own skills patiently. It works, but the higher ranked player will either be bored doing the lower levels (his weapon will kill 2-3 times faster than yours) or you will learn quickly how to dodge and evade higher ranked monsters quickly.
Good luck. There is no free Lunch/Crown