It is advised, especially if you're new, to take a look at this mock application made in order to get an idea for how applications work: Mock application.
Note: You cannot make a wordbubble or page for your character until they are accepted and the template has been posted on the application page.
1. Your character can be any type of bender or non-bender, except the Avatar of course. All char
2. Your application must be at least THREE PARAGRAPHS (for just the history) containing five sentences in each. Please break these paragraphs up - it makes it easier to read. It must be in depth and detailed on why your character wanted to become a citizen of Republic City and how they got there. All histories must comply with our histories that explain what happened between the age of Korra and the current time. The World History section of the navigation bar is where the story can be found. This is especially important if you desire a character from the Southern Water Tribe or Earth Kingdom since those countries no longer possess those names.
3. YOU MUST SHOW A PICTURE OF YOUR CHARACTER.
4. Your character CANNOT make his/her own tribe, be the avatar, blessed by the moon spirit (as there can only be one and there is), or be royalty (example: firelord's child); etc.
5. You must give, but are not limited to, the following information:
Appearance: (Image and description)
History: (Three paragraphs, detailed, containing at least seven sentences)
A guide of character alignments can be seen here.
6. For powers/abilities for your character if they are a bender/non-bender, you do not get to choose what you have just yet. Each bending type(and Non-benders) have a preset list of initial powers, and then progresses to obtain more over time. (See here) Meaning characters cannot start out as master benders capable of abilities such as bloodbending or lightningbending.
7. 5-6 is the normal age for a child to first use their bending; they're likely to try to bend if they know they have close relatives that are benders. However, if the character is in a situation where they wouldn't try (such as an airbender birthed by two non-benders), it's fair to say they do not learn until 8-9. Nine is the absolute limit for a person to know whether they're a bender or not.
8. If unapproved and you go more than seven days without editing on your application it will be archived.
9. Your character is YOUR character, meaning it is what you make he/she out to be. DO NOT steal ideas from other characters on here. BE ORIGINAL.
10. If you desire your character to join any of the listed factions on the navigation bar, you must receive the approval of the owner of the faction leader. Ex: You must ask Wingstrike, the owner of Ming He if your character may join the Yin Shi. Faction membership is highly recommended for first time characters since they provide an easy way to get involved in roleplaying on the wiki. They allow your character to go on wonderful adventures and bond with others. Faction involvement is also the best way to earn Event Points which can be used for all sorts of things. Molding a character for one of the factions is certainly something to consider and a smart move to make.
11. Seeing as how the entire point of citizenship applications is to create new residents for the city, it is clearly forbidden for users to make characters who were born in the city without a special prize that would allow them to do so.
Special rule: So, as far as character names go, they must fit the world and the themes explained below. Due to rarity of last names in Avatar as they were generally only present in nobility and other wealthy families, if you choose to have a last name for your character, you must put the work in to make the name fit his/her background. Keep in mind, a last name is not necessary and is a very uncommon thing.
Note: For reference if you do want a last name, the Earth and Fire nation have mainly a Chinese and somewhat Japanese theme to names, the Water tribes have Inuit (Eskimo) based names and the Air nomads do not have nobility, as they are nomads, and as such if your character is part of the nomads, they wouldn't have a last name without good reason, such as being part of an Earth Republic family while still being an airbender.
If you need help coming up with an Avatar themed character name, click here: http://forums.avatarspirit.net/index.php?topic=10938.0