You can add an OnClickListener to your button, and if the button is clicked start a browser via an intent that points to facebook. This would only let the user go to facebook and do whatever she wants there, if you want to interact with some facebook api you have to go another route.
button.setOnClickListener(new OnClickListener() {
public void onClick(View view) {
Intent intent = new Intent(Intent.ACTION_VIEW, Uri.parse("http://facebook.com"));
startActivity(intent);
}
});
Disclaimer
The code is not tested completly but it must be something like that. If you spot an error feel free to correct it.