Paresh Mayani’s answer is mostly correct. Simply use a Broadcast Intent to let the system and all the other apps choose in what way the content is going to be shared.
To share text use the following code:
String message = "Text I want to share.";
Intent share = new Intent(Intent.ACTION_SEND);
share.setType("text/plain");
share.putExtra(Intent.EXTRA_TEXT, message);
startActivity(Intent.createChooser(share, "Title of the dialog the system will open"));