C++ implementation question

I was wondering if you guys can help me out with a design issue I am
running into.

I have a class that needs to maintain a mapping between a table name
and its corresponding list of columns.

The column class is defined thusly:

struct Column
{
    enum Type
    {
        BOOL = 1,
        INT = 2,
        FLOAT = 3
        // etc. and so on
    };
    Type type(); // returns the type of the column
};

There is also an API that gives me the value of a column given a
column pointer. Its overloaded for various types like:

APIPtr->get(Column* c, <overloads_for_various_types>& colvalue);

/*
APIPtr->get(Column* c, int& value);
APIPtr->get(Column* c, char*& value);
// etc
*/

I went down this direction:

class TableHandler
{
    std::map<std::string, std::vector<Column*> > Table2ColumnMap;
    Table2ColumnMap table2Col_; // this map is set at construction time
public:
    TableHandler()
    {
        Column* c1 = APIPtr->getColDetailsFromSomewhere("COLNAME1");
        Column* c2 = APIPtr->getColDetailsFromSomewhere("COLNAME2");
        Column* c3 = APIPtr->getColDetailsFromSomewhere("COLNAME3");
        vector<Column*> colvec;
        colvec.push_back(c1);
        colvec.push_back(c2);
        colvec.push_back(c3);
        tale2Col_.insert(std::make_pair("TABLE1", colvec));
    }
};

I was wondering if there is a way to write a method in TableHandler
that can give iteratively extract the values of all the columns given
a table name (using that APIPtr->get() thingy).

So I came all the way here:

void TableHandler::ExtractColValues(std::string const& tablename)
{
    // 1. drill into map; 2. locate associated vector of columns
    // 3. IT is at this point I am a little confused

}

As I noted in (3), each Column* already maintains an enum that is
indicative of its type. I want to write a clean mechanism to extract
the value of that column using APIPtr->get() and somehow using its
type. I just am not able to translate it into code.

Can someone point me in the right direction? Just a hint would be
appreciated -- I can expand it from there.