Calling instance of a class in Python

If you want to build a list of contacts, instead of AddContact as a class, make it a function:

def add_contact():
    newname = str(input("First name: \t"))
    newsurname = str(input("Surname: \t"))
    newage = int(input("Age: \t"))
    newmobile_no = int(input("Mobile Number: \t"))
    newhome_no = int(input("Home Number: \t"))
    newContact = People(newname, newsurname, newage, newmobile_no, newhome_no)
    return newContact

Then, you can create a list of contacts:

contacts = []
contacts.append(add_contact())
contacts.append(add_contact())

And finally, display the contacts in the list by iterating over it:

for p in contacts:
    p.DisplayContacts()

The basic problem here is that you're assuming the People class will act as a container type to hold multiple contacts, whereas you've written as a class which will hold only the attributes of a single contact.

The actual goal of your code is unclear. You switch back and forth between treating the People class as a single contact and as a collection thereof:

In the __init__ function you prepare the object to store a single contact (one person with one name, age, etc.)

class People():
    def __init__(self, name, surname, age, mobile_no, home_no):
        self.name = name
        self.surname = surname
        self.age = age
        self.mobile_no = mobile_no
        self.home_no = home_no

This function, although it is named DisplayContacts (plural), also treats the object as storing a single contact:

  def DisplayContacts(self):
      print("First Name: \t", self.name)
      print("Surname: \t", self.surname)
      print("Age: \t", self.age)
      print("Mobile Number: \t", self.mobile_no)
      print("Home Number: \t", self.home_no)

I don't know quite what this is. I think you mean to create a function rather than a class here, so I'm changing it as such. Now you read in a new contact's information and store it in a new instance of the People class:

# was class AddContact(), which makes no sense:
def AddContact():

        newname = str(input("First name: \t"))
        newsurname = str(input("Surname: \t"))
        newage = int(input("Age: \t"))
        newmobile_no = int(input("Mobile Number: \t"))
        newhome_no = int(input("Home Number: \t"))
        newContact = People(newname, newsurname, newage, newmobile_no, newhome_no) 

Now for the main program: you create a single contact by instantiating the oddly-named People class. Then you try to call this object as a function (???). This will cause an error because you haven't defined a __call__ method but it probably isn't what you meant to do in the first place. Finally, you try to use that result as an iterator. I don't know what the intention is:

newContact = People()  

# will cause an error: no People.__call__ method
result_of_calling_object_like_a_function = newContact()

# would cause another error, unless the object in question has an
# __iter__ method:
for p in result_of_calling_object_like_a_function:
    p.DisplayContacts()