In the below example I have created Dialog Animation using windowAnimation. Here I have added DialogAnimation item in style.xml folder after that I have created a new dialoglayout.xml and added a image and button then in mainlayout I have added a button. And lastly in MainActivity I have used Dialog Function and OnClickListener method. See the below example code it will clearly describe you to make Dialog Animation.

Step(1)-dialoglayot.xml-

<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent"
    android:orientation="vertical">

    <ImageView
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:src="@drawable/img"/>
    <Button
        android:id="@+id/dismiss"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:text="dismiss"/>

</LinearLayout>

Step(2)-activity_mainlayot.xml-

<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent" >

    <Button
        android:id="@+id/opendialog"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_centerHorizontal="true"
        android:layout_centerVertical="true"
        android:padding="5dp"
        android:text="Apply Here"
        tools:context=".MainActivity" />

</RelativeLayout>

Step(3)-Add DialogAnimation item in style.xml -

 <style name="DialogAnimation">
            <item name="android:windowEnterAnimation">@android:anim/slide_in_left</item>
            <item name="android:windowExitAnimation">@android:anim/slide_out_right</item>
        </style>

Step(4)-MainActivity-

public class MainActivity extends Activity {

        Button btnOpenDialog;

        @Override
        public void onCreate(Bundle savedInstanceState) {
            super.onCreate(savedInstanceState);
            setContentView(R.layout.activity_main);
            btnOpenDialog = (Button)findViewById(R.id.opendialog);
            btnOpenDialog.setOnClickListener(new View.OnClickListener(){

                @Override
                public void onClick(View v) {
                    openDialog();
                }});
        }

        private void openDialog(){
            final Dialog dialog = new Dialog(MainActivity.this);
            dialog.setTitle("Scholarship");
            dialog.setContentView(R.layout.dialoglayout);
            dialog.getWindow().getAttributes().windowAnimations = R.style.DialogAnimation;
            Button btnDismiss = (Button)dialog.getWindow().findViewById(R.id.dismiss);

            btnDismiss.setOnClickListener(new View.OnClickListener(){

                @Override
                public void onClick(View v) {
                    dialog.dismiss();
                }});

            dialog.show();
        }

    }