Since Google Play Store is not preloaded onto Remix OS for PC and there are many different instructions out there that describe how you can download and install Google Play store, I have decided to post the most updated and accurate one here.
1. Download the GMSActivator.apk, attached in this post, directly onto your Remix OS
2. Click on the downloaded file to install it (You may need to change your settings to allow installation of apps from unknown sources. Settings > Security > Device Administration)
3. Open the installed file
4. Select "Install Google Services"
5. Reboot OS.