Apache HttpClient doesn't know anything about JSON, so you'll need to construct your JSON separately. To do so, I recommend checking out the simple JSON-java library from json.org. (If "JSON-java" doesn't suit you, json.org has a big list of libraries available in different languages.)
Once you've generated your JSON, you can use something like the code below to POST it
StringRequestEntity requestEntity = new StringRequestEntity(
JSON_STRING,
"application/json",
"UTF-8");
PostMethod postMethod = new PostMethod("http://example.com/action");
postMethod.setRequestEntity(requestEntity);
int statusCode = httpClient.executeMethod(postMethod);
Edit
Note - The above answer, as asked for in the question, applies to Apache HttpClient 3.1. However, to help anyone looking for an implementation against the latest Apache client:
StringEntity requestEntity = new StringEntity(
JSON_STRING,
ContentType.APPLICATION_JSON);
HttpPost postMethod = new HttpPost("http://example.com/action");
postMethod.setEntity(requestEntity);
HttpResponse rawResponse = httpclient.execute(postMethod);