The app does not offer a typical login screen, instead you have to scan a QR code on your iPhone in order to activate your account on the desktop version of the application. Once you have done so you can begin talking to friends and continue conversations from where you left off.
To authorize WhatsApp for desktop on your computer, simply launch the app on the computer and iPhone. Then on iPhone go to Settings > WhatsApp Web > Scan QR Code. Finally scan the QR code on the desktop app with the device’s camera.