You are to do this by using a downloaded Whatsapp APK file. Download the Whatsapp APK from here http://www.techspot.com/downloads/5748-whatsapp-for-android.html (click 'Direct Download' there)
To install, first go to Settings > Security/Applictaions > and check the "Unknown Sources" check box (to allow non-Play Store applications to install). The launch the "File Manager" application or any other File Explorer/ Manager application your device is running. From there select the SD card storage location > open the "Download" folder from there > scroll to and tap the downloaded Whatsapp apk file > scroll through the terms and conditions and then tap "Install".
You will get the options "Done" and "Open" when the installation process is completed. Now tap Open > Tap "I Agree" > tap "Continue" and then enter the number you wish to use and go that route to verify and complete the activation of your Whatsapp messenger application. Please ask any question you may have on this from this very Q&A site.