Ranks
As far as applying is concerned, these are the ranks that could involve your character. There are many other ranks in existance, and the private area has a much lengthier exposition on these; however, to stop confusing everyone with my excessively long pages, here's the abbreviated version.
All other ranks are able to be achieved ICly; however, not all can be simply given out to the first person that asks. If you are interested in a particular ranking position, just talk to one of the admins about it. In all cases, especially with higher ranks, a PC involvement is preferred, and straight-out applications for certain positions may be declined if the admins are unsure of your committment/skill.
Dragonrider Ranks
Wingrider: Your average dragonrider-- the large bulk of the riders in the Weyr will be of this ranking. Duties involve taking care of their dragon, participating in Wing drills, and fighting Thread. This covers riders of all colours, ages, genders and skill levels.
Candidate: While you cannot directly apply as a Candidate, it is important to mention this rank here. If you are planning on becoming a Candidate, please consider joining as an Apprentice, Journeyman, Resident or Drudge; there is an internal Search process that must be undertaken before you become a Candidate. Do note that Candidates must be between 12 and 24 turns of age, and must not have any sort of disibility (physical or mental) that would hinder them from dragonriding.
Crafter Ranks
The crafthalls are: baker, beast, farmer, harper, healer, metal, miner, sea, smith, star, tailor, tanner, vintner, weaver, wood, and unofficially, dragonhealer.
Craftmaster: The top of the food chain in terms of crafters. They're likely to be well into their adult ages, and wholly dedicated to their craft-- and are very skilled at it. They aren't too common around the Weyr, excepting the Weyrhealer and Weyrharper positions, but some-- especially retired craftmasters, or some with particular interest in Weyrs or Dragons-- end up taking positions around the Weyr, teaching apprentices/journeymen and otherwise assisting Weyr management and production.
Journeyman: A skilled craftsman who has been recognised by their hall, and often placed by the hall to various holds and weyrs to increase their life experience. Journeymen often look for schooling under craftmasters in order to obtain their master's knots themselves. They are often placed in management positions in the weyr; that is, a journeyman beastcrafter would help coordinate the weyr's hunting activities, and so forth. It is rare for a journeyman to become a candidate, but not impossible.
Apprentice: The lowest rung of the crafter heirarchy, these are the children learning the ropes of how to perform their craft. While a large majority are taught directly at the hall, holds and weyrs alike have journeymen and masters that can begin or continue an apprentice's training. It is a common sight for candidates who did not impress to be encouraged towards apprenticeship between clutches, if only for a "second option".
Residential Ranks
(Assistant) Headwoman: The Headwoman is the main figure when it comes to internal affairs of the Weyr. The assistants often delegate the headwoman's power and duties. Generally skilled managers and organisers, they help coordinate the "inside" duties of the Weyr-- laundry, stores, education, meals, residency, candidacy, tithing, and so forth.
(Assistant) Steward: The Steward is the main figure when it comes to external affairs of the Weyr. The assistants often delegate the headwoman's power and duties. Generally skilled managers and organisers, they help coordinate the "outside" duties of the Weyr-- hunting, farming, construction, woodcutting, fishing, beast care, repairing, and so forth.
Head Cook: Someone with a lot of experience-- often a journeyman baker-- is appointed to this important position in the kitchens. They decide what the weyrfolk eat, and how to go about making sure it lands on the tables in time!
Resident: The normal folk of the Weyr, doing many untrained though very important duties. Once children reach the age of about 12, they are considered a resident, and expected to take part in as much work as everyone else. Possible vocations for residents include:
Weyrbrat: The children of the Weyr, under the age of about 12. They are largely confined to the creche, supervised by nannies and their helpers, educated by the weyrharper and assistants and entertained to the best of the staff's ability.
Drudge: The unskilled labourers, given the tasks few others want to take part in: cleaning the grubbiest of rooms, sweeping the weyrhall, taking messages from one side of the Weyr to another, and so on.