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Creating function in your controller/module/class.

It's dummy way to create it rawly, better to use ForMbuilder of prestashop.

But anyway my code works:

public function createAddressCustom(){
        if (((bool)Tools::isSubmit('create_address_custom')) == true){
            $user_address_surname = Tools::getValue('adress_surname');
            $user_address_name = Tools::getValue('adress_name');
            $user_address_address = Tools::getValue('adress_adress');
            $user_address_complement = Tools::getValue('adress_complement');
            $user_address_postcode = Tools::getValue('adress_postcode');
            $user_address_city = Tools::getValue('adress_city');
            $user_address_country = Tools::getValue('adress_country');
            /*creating address*/
            $address = new Address(null, $this->context->language->id);
            $address->lastname = trim(ucfirst($user_address_surname)); 
            $address->firstname = trim(ucfirst($user_address_name));
            $address->address1 = ucfirst($user_address_address);
            $address->address2 = ucfirst($user_address_complement);
            $address->postcode = trim($user_address_postcode);
            $address->city = ($user_address_city);
            $address->id_customer = (int) $this->context->customer->id;
            $address->id_country = (int)19;
            $address->id_state = 0;
            $address->alias = 'Mon adresse'; 
            //dump($address);
            $address->save();       
        }
    }

And .tpl file below

<form>
  <div class="form-group">
    <label for="exampleInputEmail1">Nom</label>
    <input type="text" class="form-control text-capitalize" id="" name="user_surname"  placeholder="">
  </div>
  <div class="form-group">
    <label for="exampleInputEmail1">Prenom</label>
    <input type="text" class="form-control text-capitalize" id="" name="user_name"  placeholder="">
  </div>
  <div class="form-group">
    <label for="exampleInputEmail1">Email address</label>
    <input type="email" class="form-control" id="" name="user_email" namearia-describedby="emailHelp" placeholder="Votre email">
    <small id="emailHelp" class="form-text text-muted">Nous ne partagerons jamais votre e-mail avec quelqu'un d'autre</small>
  </div>
  <div class="form-group">
    <label for="exampleInputPassword1">Password</label>
    <input type="password" class="form-control" id="" name="user_password" placeholder="Password">
  </div>
  <div class="form-group">
    <label for="exampleInputPassword1">Numero de telephone</label>
    <input type="number" class="form-control" id="" name="user_phone" placeholder="Example:0041761234567">
    <small id="emailHelp" class="form-text text-muted"></small>
  </div>
  <div class="form-group">
    <label for="exampleInputPassword1">Date de naissance</label>
    <input type="date" class="form-control" id="" name="user_birthdate" placeholder="jj/mm/aa">
    <small id="emailHelp" class="form-text text-muted">Date de votre naissance</small>
  </div>



  <button type="submit" class="btn btn-primary" name="create_user_custom" value="Save">Submit</button>
</form>

Dont forget to add phone number to ps_customer table, because I link the phone not to adress but to customer.

Also dont forget to link your tpl to the controller/module:

return $this->display(__FILE__, 'views/templates/front/create_order.tpl');
//or path you desire

P.S. just remember, you need to adapt the code to your needs, it's something as cheatsheet I wrote you and code was written to my needs.