How do I access and call Javascript Object properties and methods from C++ using V8?

I haven't tested the examples below.

But I believe it gives an example of what you want.

#include <v8.h> 
using namespace v8;
int main(int argc, char* argv[]) {
  // Create a handle scope
  HandleScope handle_scope;
  // Create a new context. 
  Handle<Context> context = Context::New();
  // Enter the created context for compiling and 
  // running the script.
  Context::Scope context_scope(context);
  // Create a new script  
  const char* script = "function MyObj() { this.myArray = []; this.myDouble = 0; this.myFunction = function(arg1,arg2) {   return (myDouble + arg1 + arg2);  } } var globalObject = new myObj();"
  // Create a string containing the JavaScript source code. 
  Handle<String> source = String::New("script");
  // Compile the source code. 
  Handle<Script> script = Script::Compile(source);
  // Running the script
  // Run the script to get the result. 
  Handle<Value> scriptresult = script->Run();
  // Convert the result to an ASCII string and print it. 
  String::AsciiValue ascii(scriptresult);
  printf("%s\n", *ascii);

  // Get the object
  Handle<Object> object = Local::Cast(context->Global()->Get(String::New("globalObject")));
  // Get the Properties 
  Handle<Value> arrayproperty = Handle::Cast(object->Get(String::New("myArray")));
  Handle<Value> doubleproperty = Handle::Cast(object->Get(String::New("myDouble")));
  String::AsciiValue ascii2(arrayproperty);
  String::AsciiValue ascii3(doubleproperty);
  printf("%s\n", *ascii2);
  printf("%s\n", *ascii3);
  // Call the function
  Handle fun_to_call = Handle::Cast(object->Get(String::New("myFunction"))); 
  int argcount = 0;
  Handle argarray[] = NULL;

  Handle functionresult = fun_to_call->Call(object, argcount, argarray); 
 // argcount and argarray are your standard arguments to a function

  return 0;


}

As for how to modify the array I believe it would be using

// Get the object
Handle<Object> object = Local::Cast(context->Global()->Get(String::New("globalObject")))1;

//Initialise array
int num[4] = {1,2,3,4};
v8::Local<v8::Array> arguments = v8::Array::New(num); 
for (int i = 0; i < args; i++) { 
  arguments.Set(v8::Number::New(i), v8::String::New(args[i])); 
} 

// Set Array
object->Set(v8::String::New("myArray"), arguments); 

References

CodeProject Using V8

Connecting C++ to Javascript bungeeconnect

Google V8 Shell Sample Code

Google V8 Header File

V8 Users Mailing List Can you populate a v8::Array from C++? Thread