[android] How to copy text programmatically in my Android app?

Use ClipboardManager#setPrimaryClip method:

import android.content.ClipboardManager;

// ...

ClipboardManager clipboard = (ClipboardManager) getSystemService(CLIPBOARD_SERVICE); 
ClipData clip = ClipData.newPlainText("label", "Text to copy");
clipboard.setPrimaryClip(clip);

ClipboardManager API reference