Aye - pause > nul.
As mentioned, this isn't portable. Even if you only ever intend to run it on Windows, I think it's good practice to use standard language features... I'd definitely suggest having a look at the link dwks posted.
Your program looks like it'll do what it's meant to, but I do have a couple of comments:
You can use float here. Float is smaller (4 bytes compared to 8 bytes). It is less precise and has a smaller range but it is plenty for your program.
double grade_one, grade_two, final_grade;
You could even use ints for grade_one and grade_two, but you'd always get an int out because this calculation chops off the fractional part:
This is because two ints added together divided by another int give you an int.
final_grade = (grade_one + grade_two)/2;
Using a cast:
Horrible but works:
final_grade = (static_cast<float>(grade_one + grade_two))/2;
There's nothing to gain by using ints, but I just thought I'd mention it in case you tried to use them before and couldn't.
final_grade = (grade_one + grade_two)/2.0;
Other comment is:
You know you can insert newlines with \n? You don't need to repeatedly use endl:
cout << "MyLastName Grade-o-Matic v1.0" << endl << endl << endl;
It's still a good plan to have the last newline as an endl, as endl flushes the output buffer.
cout << "MyLastName Grade-o-Matic v1.0\n\n" << endl;