In the below example I have created set wallpaper app. Here I have added two button and ImageView in activity_main.xml layout. In MainActivity I have used setOnClickListener method , displayWallpaper() and Toast function, and I have also used BitMap class for loding Imgae on backgraund screen. You can see below example code it clearly describe you "How to create set wallpaper app in android”.
Step(1)activity_main.xml -
  

 <?xml version="1.0" encoding="utf-8"?>
<LinearLayout 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"
    android:padding="16dp"
    android:orientation="vertical"
    tools:context="com.blogspot.android_er.androidwallpaper.MainActivity">

    <Button
        android:id="@+id/display"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_marginTop="8dp"
        android:layout_gravity="center"
        android:textColor="#2d53e9"
        android:textAlignment="center"
        android:textSize="14dp"
        android:background="#d8a0e4"
        android:text="Show Wallpaper"/>
    <Button
        android:id="@+id/set"
        android:layout_marginTop="8dp"
        android:textColor="#2d53e9"
        android:textSize="14dp"
        android:background="#e4d6a0"

    android:layout_gravity="center"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:text="Set Wallpaper"/>
    <ImageView
        android:id="@+id/image"
        android:layout_width="match_parent"
        android:layout_height="match_parent" />
</LinearLayout>

Step(2)-MainActivity-
 

public class MainActivity extends AppCompatActivity {


        ImageView imageWallpaper;
        Button btnLoadWallpaper, btnDisplayWallpaper;

        private static final int RQS_OPEN_IMAGE = 1;

        @Override
        protected void onCreate(Bundle savedInstanceState) {
            super.onCreate(savedInstanceState);
            setContentView(R.layout.activity_main);

            imageWallpaper = (ImageView)findViewById(R.id.image);

            btnDisplayWallpaper = (Button)findViewById(R.id.display);
            btnDisplayWallpaper.setOnClickListener(new View.OnClickListener() {
                @Override
                public void onClick(View v) {
                    displayWallpaper();
                }
            });

            btnLoadWallpaper = (Button)findViewById(R.id.set);
            btnLoadWallpaper.setOnClickListener(btnLoadWallpaperOnClickListener);
            displayWallpaper();

        }

        View.OnClickListener btnLoadWallpaperOnClickListener = new View.OnClickListener() {

            @Override
            public void onClick(View v) {
                Intent intent = new Intent();

                if (Build.VERSION.SDK_INT >=
                        Build.VERSION_CODES.KITKAT) {
                    intent.setAction(Intent.ACTION_OPEN_DOCUMENT);
                } else {
                    intent.setAction(Intent.ACTION_GET_CONTENT);
                }

                intent.addCategory(Intent.CATEGORY_OPENABLE);

                // set MIME type for image
                intent.setType("image/*");

                startActivityForResult(intent, RQS_OPEN_IMAGE);
            }
        };

        private void displayWallpaper(){
            WallpaperManager myWallpaperManager =
                    WallpaperManager.getInstance(getApplicationContext());
            Drawable drawableWallpaper = myWallpaperManager.getDrawable();
            imageWallpaper.setImageDrawable(drawableWallpaper);

            Toast.makeText(this,
                    drawableWallpaper.getMinimumWidth() + " x " + drawableWallpaper.getMinimumHeight()
                            + "\n" +
                            drawableWallpaper.getIntrinsicWidth() + " x " + drawableWallpaper.getIntrinsicHeight(),
                    Toast.LENGTH_LONG).show();
        }

        @Override
        protected void onActivityResult(int requestCode, int resultCode, Intent data) {
            if (resultCode == Activity.RESULT_OK) {
                if (requestCode == RQS_OPEN_IMAGE) {
                    Uri dataUri = data.getData();
                    Uri wallpaperUri = dataUri;
                    Toast.makeText(this, wallpaperUri.toString(), Toast.LENGTH_LONG).show();

                    Bitmap newOriginalBM= loadBitmap(dataUri);;
                    reloadWallpaper(newOriginalBM);
                }
            }
        }

        private Bitmap loadBitmap(Uri src) {

            Bitmap bm = null;

            try {
                bm = BitmapFactory.decodeStream(
                        getBaseContext().getContentResolver().openInputStream(src));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }

            return bm;
        }

        private void reloadWallpaper(Bitmap bm){
            if(bm != null){
                WallpaperManager myWallpaperManager =
                        WallpaperManager.getInstance(getApplicationContext());

                if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.M) {
                    if(myWallpaperManager.isWallpaperSupported()){
                        try {
                            myWallpaperManager.setBitmap(bm);
                        } catch (IOException e) {
                            e.printStackTrace();
                        }
                    }else{
                        Toast.makeText(MainActivity.this,
                                "isWallpaperSupported() NOT SUPPORTED",
                                Toast.LENGTH_LONG).show();
                    }
                }else{
                    try {
                        myWallpaperManager.setBitmap(bm);
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                }
            }else{
                Toast.makeText(MainActivity.this, "bm == null", Toast.LENGTH_LONG).show();
            }
        }
    }