The first version:
function[0] = 42; // version 1
may or may not insert the value 42 into the map. If the key 0 exists, then it will assign 42 to that key, overwriting whatever value that key had. Otherwise it inserts the key/value pair.
The insert functions:
function.insert(std::map<int, int>::value_type(0, 42)); // version 2
function.insert(std::pair<int, int>(0, 42)); // version 3
function.insert(std::make_pair(0, 42)); // version 4
on the other hand, don't do anything if the key 0 already exists in the map. If the key doesn't exist, it inserts the key/value pair.
The three insert functions are almost identical. std::map<int, int>::value_type is the typedef for std::pair<const int, int>, and std::make_pair() obviously produces a std::pair<> via template deduction magic. The end result, however, should be the same for versions 2, 3, and 4.
Which one would I use? I personally prefer version 1; it's concise and "natural". Of course, if its overwriting behavior is not desired, then I would prefer version 4, since it requires less typing than versions 2 and 3. I don't know if there is a single de facto way of inserting key/value pairs into a std::map.
Another way to insert values into a map via one of its constructors:
std::map<int, int> quadratic_func;
quadratic_func[0] = 0;
quadratic_func[1] = 1;
quadratic_func[2] = 4;
quadratic_func[3] = 9;
std::map<int, int> my_func(quadratic_func.begin(), quadratic_func.end());