All requests must be authenticated using OAuth. Please consult http://oauth.net/documentation/getting-started/ for an introduction to OAuth. OAuth libraries for different programming languages are listed at http://oauth.net/code/.
Long story short, you need a consumer_key and a consumer_secret. The consumer_key is a little bit like your username and is part of the request. As for the consumer_secret, well, it's a secret and must be kept to yourself.
The consumer_secret is used to generate a signature for the request. The signature is included in the request itself just before you send it. When we receive it, we generate the signature with your consumer_secret and if it matches the signature you specified, we know the request comes from you.