I have a string whose content is a function name, how to refer to the corresponding function in Python?

Since you are taking user input, the safest way is to define exactly what is valid input:

dispatcher={'add':add}
w='add'
try:
    function=dispatcher[w]
except KeyError:
    raise ValueError('invalid input')

If you want to evaluate strings like 'add(3,4)', you could use safe eval:

eval('add(3,4)',{'__builtins__':None},dispatcher)

eval in general could be dangerous when applied to user input. The above is safer since __builtins__ is disabled and locals is restricted to dispatcher. Someone cleverer than I might be able to still cause trouble, but I couldn't tell you how to do it.

WARNING: Even eval(..., {'__builtins__':None}, dispatcher) is unsafe to be applied to user input. A malicious user could run arbitrary functions on your machine if given the opportunity to have his string evaluated by eval.

One safe way is to map from names to functions. It's safer than using eval.

function_mappings = {
        'add': add,
}

def select_function():
    while True:
        try:
            return function_mappings[raw_input('Please input the function you want to use')]
        except KeyError:
            print 'Invalid function, try again.'

The built-in function eval will do what you want. All the usual warnings about executing arbitrary user-supplied code apply.

If there are a finite number of predefined functions, you should avoid eval and use a lookup table instead (i.e. Dict). Never trust your users.