Why on earth would you write such a thing, instead of using std::string? Since your question is tagged C++.
int main(int argc, char* argv[])
{
std::string a = " 'Fools' day' ";
std::string b(a.begin() + 2, std::find(a.begin() + 2, a.end(), ' '));
std::cout << b;
std::cin.get();
}
Edit: Oh wait a second, you want to read a string within a string? Just use escaped double quotes, e.g.
int main(int argc, char* argv[]) {
std::string a = " \"Fool's day\" ";
auto it = std::find(a.begin(), a.end(), '"');
std::string b(it, std::find(it, a.end(), '"');
std::cout << b;
}
If the user put the string in, they won't have to escape single quotes, although they would have to escape double quotes, and you'd have to make your own system for that.