First, you’ll need to register an application now if you haven’t already.
Click your username in the upper right hand corner and select “My Applications” from the drop down.
Then, create a new application. After your application is specified, you have your consumer key and secret.
Next, have the web site create your access token – there’s a button there (I forget its exact wording).
At that point, you have a consumer key & secret and an access key & secret, which is what you need for your server process to authenticate.
If you are using Java, then the code will look something like:
tf = new TwitterFactory();
connection = tf.getInstance();
AccessToken at = new AccessToken("access-key-goes-here", "access-secret-goes-here");
With the keys and secrets substituted into the calls, of course.