In the beginning of the forum, the Leader and Captain Slots will be open. This will allow most of the first people to join to gain powerful positions early on in the game. This includes the 13 Captains of the Seireitei Court Guard Squad, the Vizard Leader, Quincy Master, Human Ace, and Arrancar Leader.
To gain rank you must prove yourself in someway. One would be gaining the next level on your Zanpaktou, or learning a new special attack. Other, more formal ways would be proving yourself a good Soldier, and being a Suck up. Once both an Admin and your Superior has agreed, you will be given a higher rank.
They're are also a limit to how many of a certain rank there can be. Example, there can only be one Captain and one Second in command. Then, there can be 5 Officers, a 3rd, 4th, 5th, 6th, and 7th Seat. The rest are unlimited amount.
For Vizards, there is a total of 7 Max overall. One Leader, 2 Lords, and the rest can either be Shinigami, Vizards, or Knights.
For the Arrancar, there are unlimited amount of Numeros and Privarons. However, for the Espada, there is a limit of 9, 10-2 Espadas.
Then, the 1st Espada, or the Arrancar Leader, is also a one only rank.
Finally, for all Hollows, there is no limit. For Quincys and Humans there is also no limit, except for only one Quincy Master and one Human Ace.
Now, if there is a slot open for a Leader/Captain, you may Claim it. For the rest of the ranks, you are assigned by your superior. Now, you may request a rank, and you may or may not get it. That is all for ranking.