Tap the download button and wait for the file to finish. The download name should be something like hlonelygirl_v1.0.1.apk .
If you are looking to download the APK for Android, version 1.0.1 is an older release, as newer versions like 1.0.5 or 4.5.0 are now available on major distribution platforms. -H- Lonely Girl APK v1.0.1 Download for Android