How to dynamically build a JSON object?

I am new to Python and I am playing with JSON data. I would like to dynamically build a JSON object by adding some key-value to an existing JSON object.

I tried the following but I get TypeError: 'str' object does not support item assignment:

import json

json_data = json.dumps({})
json_data["key"] = "value"

print 'JSON: ', json_data