For the implement asynchronous call you can use following library with react-redux

1. redux-thunk
2. redux-promise
3. redux-saga

You can learn asynchronous call handling using library documentation

If you are using vanilla ReactJS and your App does not need any Flux or Redux to control the state of the App, you can use React life-cycle method componentWillMount for that with builtin fetch method or library like axios

If your Application needs Flux or Redux then I personally recommend Redux over Flux and you can use redux-thunk middleware for that. for example

const INCREMENT_COUNTER = 'INCREMENT_COUNTER';

function increment() {
  return {
    type: INCREMENT_COUNTER
  };
}

function incrementAsync() {
  return dispatch => {
    setTimeout(() => {
      // Yay! Can invoke sync or async actions with `dispatch`
      dispatch(increment());
    }, 1000);
  };
}

For more see http://redux.js.org/docs/advanced/AsyncActions.html

Here is the documentation for how to use async actions : http://redux.js.org/docs/advanced/AsyncActions.html

You define it like so when configuring the store:

const store = createStore(
  rootReducer,
  applyMiddleware(
    thunkMiddleware
  )
)

And you use it in the actions like so:

function fetchAction(data) {
  // Return a function, this function will be activated the the thunk middleware with dispatch as parameter
  return function (dispatch) {
    // Dispatch some action before fetch (like setting loading)
    dispatch(requestData(data));

    // return a promise of the fetch
    return fetch('yoururl')
      .then(response => response.json())
      .then(json =>
        // dispatch a new action when you get your data
        dispatch(receivedData(data,json))
      ).catch (e = > 
        // you can also dispatch an error
        dispatch(errorData(data,e));
      )

  }
}