The first method is to enable app installation from Unknown sources.
Go to the Settings> Security> check Unknown sources to enable the App installation from Unknown sources.
Now, once the flashing of .apk files is enabled from unknown sources, you can open the .apk file directly on your Android device and install the same.
The second method to install the APK file by using an APK installer application.
To install the .apk file, you need to transfer the .apk file to internal or external storage of the device. For making this you can use a file manager to access the .apk file or a suitable application from the Play Store that will list all the .apk files existent on your Xperia device.
Now, copy the .apk file to the internal or external storage of your device.
Now, open the app and let the application scan all the .apk files available on the device.
Once the scanning operation is done, select the application that you want to be installed and then tap the Install button.
On the installation screen you need select Install to start the installation of the application. Note that, if you see the Next instead of Install button, click through Next and the Install button will be displayed.
The last method to install the .apk file is to use a File manager application:
First, you need to transfer the .apk file to internal or external storage of the Xperia device.
Now, download the file manager application such as ES File Explorer from Google Play Store.
Next, by using the file manager application, you need open the folder where the downloaded .apk file is saved on the Xperia device.
Select the APK file that you want to be installed.
Next, select Install to start the flashing process.
On the flashing process select Install to start the installation of the application. If you see Next button instead of Install, click throught Next, and you will get the Install button.
Now, the new Android L theme apk file should be installed on your Sony Xperia device.