How do I check my template class is of a specific classtype?

If you don't care about compile-time, you may use boost::is_same.

bool isString = boost::is_same<T, std::string>::value;

As of C++11, this is now part of the standard library

bool isString = std::is_same<T, std::string>::value

Instead of checking for the type use specializations. Otherwise, don't use templates.

template<class T> int foo(T a) {
      // generic implementation
}
template<> int foo(SpecialType a) {
  // will be selected by compiler 
}

SpecialType x;
OtherType y;
foo(x); // calls second, specialized version
foo(y); // calls generic version

hmm because I had a large portion of same code until the 'specification' part.

You can use overloading, but if a large part of the code would work for any type, you might consider extracting the differing part into a separate function and overload that.

template <class T>
void specific(const T&);

void specific(const std::string&);

template <class T>
void something(const T& t)
{
    //code that works on all types
    specific(t);
    //more code that works on all types
}

I suppose you could use the std::type_info returned by the typeid operator