Once a visitor fills a Leads Form on your Landing Page their details are stored as leads on the Platform but are not automatically entered as Contacts.
If you wish to integrate their details into your Contacts Data Base, in order to among others be in touch with them in the future via SMS, go to the Landing Page Settings Screen:
There under Additional Actions you will find the option to add lead details to Contacts:
Once you tick the checkbox a Drop Down menu with a list of all you Contact Groups will open for you to select to which Group you wish to affiliate the leads.
To integrate the lead a Group must be chosen. If you have yet created the designated Group you wish to use, go first to the Contacts module:
and press there on Create Group: