How to implement the Android ActionBar back button

Add this code in your on create activity Method 

@Overrideprotected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);

    setSupportActionBar(toolbar);

    getSupportActionBar().setDisplayHomeAsUpEnabled(true);
    getSupportActionBar().setDisplayShowHomeEnabled(true);

}

then call this method

@Overridepublic boolean onOptionsItemSelected(MenuItem item) {
    switch (item.getItemId()) {
        case android.R.id.home:
            finish();
            return true;
        default:
            return super.onOptionsItemSelected(item);
    }
}

this is default support action bar if you want your own then use own tool 
bar in your xml thanks