To fulfill the download, you will need to allow permission for your device to download APK files, and also permission to download from this specific website.See this article on How to Download APK Files for a more detailed guide. Once you have found the version you need, download it.You will need to check your version of Android before you decide which version of the Play Store you download. Certain versions only run on the newest versions of Android. To download Play Store for your Android device, you will need to select the appropriate version for your device. This particular download is from APKMirror, one of the most trusted sites for downloading APK files.
Downloading an APK file is straight forward. The link on this page is to the Google Play Store APK Download for Android.