how to initialize string pointer?

A std::string pointer has to point to an std::string object. What it actually points to depends on your use case. For example:

std::string s("value"); // initialize a string
std::string* p = &s; // p points to s

In the above example, p points to a local string with automatic storage duration. When it it gets destroyed, anything that points to it will point to garbage.

You can also make the pointer point to a dynamically allocated string, in which case you are in charge of releasing the resources when you are done:

std::string* p = new std::string("value"); // p points to dynamically allocated string
// ....
delete p; // release resources when done

You would be advised to use smart pointers instead of raw pointers to dynamically allocated objects.

As array is an array of strings you could try this:

int main()
{
  string *array = new string[1]; 
  array[1] = "value";
  return 0;
}

You can explicitly convert the literal to a string:

 std::string array[] = {std::string("value")};

Note that you have to define this as an array, not a pointer though. Of course, an array mostly makes sense if you have more than one element, like:

string array[] = {string("value1"), string("value2"), string("etc")};