I need to create a class that connect to Twitter in Android without using any external libraries… Does anyone knows how to do it ?
You’ll need first to understand how OAuth works. Search the web for “OAuth tutorial” or “understanding OAuth” or “implementing OAuth” and you’ll find some useful materials.
Once you’ve got that bit down, you’ll need to write code first of all which gets an OAuth access token for your application. Following that you should look into how to sign HTTP requests. After that you should be able to access the Twitter API.
This isn’t by any means a recommended path, though. Writing your own OAuth client is easy to get wrong and difficult to get right. There are libraries available which have done the hard work; use them!