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.
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.
3. YOU MUST EITHER SHOW A PICTURE OF YOUR CHARACTER OR WRITE A DESCRIPTION. PHOTO IS PREFERRED.
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: (Photo or description)
History: (Three paragraphs, detailed, containing at least seven sentences)
A guide of character alignments can be seen here.
Optional types of information would be:
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)
7. If unapproved and you go more than seven days without editing on your application it will be archived.
8. 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.
9. Lastly, we recommend signing the bottom of your application. But this is not a strict requirement. (Use ~~~~ to sign with your signature.)
Special rule: So, as far as character names go, it is pretty much anything goes for first names. However, 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 kingdom 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