How can I get a value from a map?

map.at("key") throws exception if missing key.

If k does not match the key of any element in the container, the function throws an out_of_range exception.

http://www.cplusplus.com/reference/map/map/at/

std::map::operator[] is a non-const member function, and you have a const reference.

You either need to change the signature of function or do:

MAP::const_iterator pos = map.find("string");
if (pos == map.end()) {
    //handle the error
} else {
    std::string value = pos->second;
    ...
}

operator[] handles the error by adding a default-constructed value to the map and returning a reference to it. This is no use when all you have is a const reference, so you will need to do something different.

You could ignore the possibility and write string value = map.find("string")->second;, if your program logic somehow guarantees that "string" is already a key. The obvious problem is that if you're wrong then you get undefined behavior.

The answer by Steve Jessop explains well, why you can't use std::map::operator[] on a const std::map. Gabe Rainbow's answer suggests a nice alternative. I'd just like to provide some example code on how to use map::at(). So, here is an enhanced example of your function():

void function(const MAP &map, const std::string &findMe) {
    try {
        const std::string& value = map.at(findMe);
        std::cout << "Value of key \"" << findMe.c_str() << "\": " << value.c_str() << std::endl;
        // TODO: Handle the element found.
    }
    catch (const std::out_of_range&) {
        std::cout << "Key \"" << findMe.c_str() << "\" not found" << std::endl;
        // TODO: Deal with the missing element.
    }
}

And here is an example main() function:

int main() {
    MAP valueMap;
    valueMap["string"] = "abc";
    function(valueMap, "string");
    function(valueMap, "strong");
    return 0;
}

Output:

Value of key "string": abc
Key "strong" not found

Code on Ideone