How can I add a third button to an Android Alert Dialog?

When you are creating the dialog, add something like this to the builder:

builder = new AlertDialog.Builder(context);
builder.setTitle("Test");
builder.setIcon(R.drawable.icon);
builder.setMessage("test");
builder.setPositiveButton("Call Now",
        new DialogInterface.OnClickListener()
        {
            public void onClick(DialogInterface dialog, int id)
            {
                dialog.cancel();
            }
        });

builder.setNeutralButton("Setup",
        new DialogInterface.OnClickListener()
        {
            public void onClick(DialogInterface dialog, int id)
            {
                context.startActivity(new Intent(context, Setup.class));
                //dialog.cancel();
            }
        });

builder.setNegativeButton("Exit",
        new DialogInterface.OnClickListener()
        {
            public void onClick(DialogInterface dialog, int id)
            {
                dialog.cancel();
            }
        });
builder.create().show();

This code snippet should help explain the three different buttons you can use:

    alertDialog = new AlertDialog.Builder(this).create();

    alertDialog.setTitle("Dialog Button");

    alertDialog.setMessage("This is a three-button dialog!");

    alertDialog.setButton(AlertDialog.BUTTON_POSITIVE, "Button 1 Text", new DialogInterface.OnClickListener() {

      public void onClick(DialogInterface dialog, int id) {

        //...

    } }); 

    alertDialog.setButton(AlertDialog.BUTTON_NEGATIVE, "Button 2 Text", new DialogInterface.OnClickListener() {

      public void onClick(DialogInterface dialog, int id) {

        //...

    }}); 

    alertDialog.setButton(AlertDialog.BUTTON_NEUTRAL, "Button 3 Text", new DialogInterface.OnClickListener() {

      public void onClick(DialogInterface dialog, int id) {

        //...

    }});