Simple Information:
-To join a guild academy, you must go to a guild manager in either elderine/rouman/uruga and click "Academy" then "Enroll"
-Select the guild which you wish to enroll in and select "Enroll Academy" to join.
-You may also join an academy by performing the following steps: (Credits go to autarchaurzel for notifying me of this)

1) Click on the community tab on the bottom right of your screen or the "f" key.
2) Click on the Guild Academy tab.
3) Click on "Enroll" at the bottom left of the Academy page.
4) A pop up will show asking for a guild name, type in the guild name you wish to join and you will be enrolled automatically into that academy.

-You must be level 39 or lower and guildless in order to join an Academy.
-Any guild can use the guild storage now, therefore being able to use the academy to its fullest function.

Step1: Create a new guild 

Create a new guild, yes you still need 300s.

Step2: Guild Storage

Deposit items and money into the guild storage. Only the guild master will be able to withdraw the guild storage! Any other guild members will be able to deposit items into the guild storage but they are not allowed to withdraw. Any items or money you have in the guild storage can be used as rewards for the academy. 

Step3: Setting up Rewards & Obtaining Rewards

Only the Guild master will be able to set rewards. Remember, you may only use items that are in the guild storage as rewards. For example. You cannot set up the reward to give each level up 100s if you only have 10s in the storage (insufficient funds) or set up an item reward of 5 preserved signs if you only have 1 preserved sign in the guild storage. Please be aware when setting up money rewards, the academy players will receive how ever much money you set up each level, not every 5 levels. (example: I set my money reward for 10~15 at 5s, the academy players will recieve 5s each time they level up from lvl 10, 11, 12, 13, 14, 15)

When an academy player levels up, the reward will be automatically transferred to his or her "Reward Inventory" which can be found in your inventory next to the Premium Item bag and the money reward will be transferred directly to their inventory

Under the academy tab, you will see the master of the guild listed.

Check the guild ranking to see your guild in the list. You will receive points each time an academy player levels up.

Leaving an Academy:

Talk to a guild manager in either elderine/rouman/uruga and click on the academy.

Then click on "Leave"

You must have been in the academy for at least an hour to be able to leave it, otherwise you must wait til that hour passes before you may leave the academy.

Benefits for Academy Players: 
-Receive Rewards that are set up by the Guild Master each time you level.
-Each time an academy guildie levels up, the entire guild academy and the guild will receive a "Guild buff" which increase damage and defense by 5%. The buff will last for approximately 45minutes. Each time a player levels the remaining time will be added with an additional 45 minutes for each other level up by any academy players. (example: there is a guild buff going on already and it is at 25minutes, another academy player levels up and 45 minutes is added on top of the 25 minutes making it a 1hour and 10minute buff. 
-If the Guild Master is around or near any academy guildies, the academy guildies will get an increase in damage and defense.

Benefits for Academy Masters:
-You are able to teleport to an academy student via the academy page. Click on their name and then select "warp to player"
-If your academy is rank 2-10 You will automatically have a 7% dmg/def buff which will also increase any guild and academy members that are around or near you. (useful in wars and pvp)
-If your academy is rank 1, you will automatically have a 10% dmg/def buff which will increase any guild and academy members around or near you, I believe they will get it even if they are on the same map as you.

Notes:

-The academy master will have a glow around him/her to signify that they are the master of the academy.
-If you switch guild masters you must also select "Masters right transfer" in order to be able to access the academy reward settings and withdraw from guild storage.
-You may have a different Master of the guild and Master of the academy. Simply give the "Master right transfer" to a guildie who is an admin and online at the time in order to give him the rights to set Academy Rewards.
-Guild members may talk in both Guild Chat and Academy Chat, but Academy players can only talk in Academy Chat and cannot talk in Guild Chat. 
-Maximum number of players allowed in an academy is 50.(credits to DBK)

Credits go to chelekat.