How to create a Back Button in Material Design

try this

in on create:

getSupportActionBar().setDisplayHomeAsUpEnabled(true);

in your activity class (assuming you want to close this activity)

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

Material Design Tutorial This will give you brief idea how to implement material app.

If you are using ActionBarActivity with AppCompat Theme use:

getSupportActionBar().setDisplayHomeAsUpEnabled(true);

Also you may have to call setHomeButtonEnabled(true) in same manner. It will look like this:

in your onCreate add these lines

getSupportActionBar().setDisplayHomeAsUpEnabled(true);
getSupportActionBar().setHomeButtonEnabled(true);

for back navigation you have to define back navigation actiity on your AndroidMnifest.xml

<activity 
android:name=".CurrentActivity" 
android:label="@string/app_name"
android:parentActivityName=".BackActivity">
</activity>