First, checkout this section of the React docs: https://facebook.github.io/react/docs/forms.html#handling-multiple-inputs. If you totally grokked that section of the docs, then you're all set! If you're still unsure about what was going on there, this is for you!
I very often see folks get tripped up when there are multiple form inputs to handle in a single component.
For example, consider a Login form. There's a good chance it will look some thing like this: