Do you mean to say how do I use this stuff?
You can find the documentation here or there's a Get Started section at the right of this page.
For example if you want to see a list of users you could send a web request to http://api.stackoverflow.com/1.0/users and parse then JSON response.
Now if you want to find out details about a particular user lets say your details http://stackoverflow.com/users/566610/jared
Do you see the number 566610 thats the id. Every question, answer, comment ,or user has a id.
So here you need to send your web request to http://api.stackoverflow.com/1.0/users/566610
Your JSON response :
{
"total": 1,
"page": 1,
"pagesize": 30,
"users": [
{
"user_id": 566610,
"user_type": "registered",
"creation_date": 1294388578,
"display_name": "Jared",
"reputation": 28,
"email_hash": "e51f7fdd3c09fc9246278abf89f1881e",
"age": 19,
"last_access_date": 1294538702,
"website_url": "http://wphax.com",
"location": "Wisconsin, US",
"about_me": "<p>Freelance WordPress Expert</p>\n",
"question_count": 2,
"answer_count": 2,
"view_count": 1,
"up_vote_count": 0,
"down_vote_count": 0,
"association_id": "d0249d62-3c97-4b50-9df1-8c7f377846f6",
"user_questions_url": "/users/566610/questions",
"user_answers_url": "/users/566610/answers",
"user_favorites_url": "/users/566610/favorites",
"user_tags_url": "/users/566610/tags",
"user_badges_url": "/users/566610/badges",
"user_timeline_url": "/users/566610/timeline",
"user_mentioned_url": "/users/566610/mentioned",
"user_comments_url": "/users/566610/comments",
"user_reputation_url": "/users/566610/reputation",
"badge_counts": {
"gold": 0,
"silver": 0,
"bronze": 4
}
}
]
}
Take one more example. Lets assume we want to find out list of questions for this you should send your web request to http://api.stackoverflow.com/1.0/questions
and if you want questions related to a particular tag for example wordpress
your url will be http://api.stackoverflow.com/1.0/questions?tagged=wordpress
And once you have finished with your application you can register for an API key.
Read How API Keys Work for more details.
Edit :
You can use StackAPI which is an interactive way to explore the API of the stack family of sites.
Edit 1 :
You can find list of libraries here.
I hope this helps.