You'll need to add the following to your dependencies:
compile 'com.google.firebase:firebase-ads:10.2.1'
and then put this in the same file.
apply plugin: 'com.google.gms.google-services'
Next you'll need to add relevant information into your strings.xml.
<string name="banner_ad_unit_id">ca-app-pub-####/####</string>
Next place an adview wherever you want it and style it just like any other view.
<com.google.android.gms.ads.AdView
android:id="@+id/adView"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_centerHorizontal="true"
android:layout_alignParentBottom="true"
ads:adSize="BANNER"
ads:adUnitId="@string/banner_ad_unit_id">
</com.google.android.gms.ads.AdView>
And last but not least, throw this in your onCreate.
MobileAds.initialize(getApplicationContext(), "ca-app-pub-YOUR_ID");
AdView mAdView = (AdView) findViewById(R.id.adView);
AdRequest adRequest = new AdRequest.Builder().build();
mAdView.loadAd(adRequest);
If you copy-pasted exactly you should now have a small banner ad. Simply place more AdViews wherever you need them for more.