Two options: download the APK, or use Google Play (coming soon).

The APK is the app installer file for Android. You can install it directly, without going through Google Play.
Tap the download button on the download page. The file is called zonkod-latest.apk.
Android will warn you that this file comes from outside Google Play. This is normal. TapSettingsin the warning, then enableAllow from this source.
Tap the downloaded file (in your notifications or Files app). TapInstall. The app installs in a few seconds.
Find the Zonkod icon in your app drawer. Tap it to open. No account, no sign-up; just start.
Yes. The APK is built from the same source code as the Google Play version. Android will still scan it for malware after install.
Zonkod will be available on Google Play soon. Once listed, installation will be a single tap, with no settings to change.