Tap on the Contacts tab in the middle of the navigation bar. Find a contact and tap on it to view its details. Tap Invite name to get WhatsApp to send them an SMS invitation to download the app.
If you use this option to invite a contact from another country, both of you may be subject to international SMS charges. You may want to send them an email to join WhatsApp instead. To do this, go to Settings Tell a Friend and then select the method of delivery.