I would suggest the following two ways:
1. One is through the below mentioned code
HttpClient httpClient = new DefaultHttpClient();
try {
    HttpPost request = new HttpPost("http://yoururl");
    StringEntity params =new StringEntity("details={\"name\":\"myname\",\"age\":\"20\"} ");
    request.addHeader("content-type", "application/json");
    request.addHeader("Accept","application/json");
    request.setEntity(params);
    HttpResponse response = httpClient.execute(request);
    // handle response here...
}catch (Exception ex) {
    // handle exception here
} finally {
    httpClient.getConnectionManager().shutdown();
}
2. Also you can make use of Gson library to convert your java classes to JSON objects.
Create a pojo class for variables you want to send as per above Example
{"name":"myname","age":"20"}
becomes
class pojo1
{
   String name;
   String age;
   //generate setter and getters
}
once you set the variables in pojo1 class you can send that using the following code
String       postUrl       = "www.site.com";// put in your url
Gson         gson          = new Gson();
HttpClient   httpClient    = HttpClientBuilder.create().build();
HttpPost     post          = new HttpPost(postUrl);
StringEntity postingString = new StringEntity(gson.toJson(pojo1));//gson.tojson() converts your pojo to json
post.setEntity(postingString);
post.setHeader("Content-type", "application/json");
HttpResponse  response = httpClient.execute(post);
and these are the imports
import org.apache.http.HttpEntity;
import org.apache.http.HttpResponse;
import org.apache.http.client.HttpClient;
import org.apache.http.client.methods.HttpPost;
import org.apache.http.entity.StringEntity;
import org.apache.http.impl.client.HttpClientBuilder;
and for GSON
import com.google.gson.Gson;