DatePicker

UPDATE 2017-05-09 I've changed the component to remove ui:inputDate - beacuse of localization and other issues introduced by Salesforce. New components needed (and present here) are: DateTimeLib, InputDate, Select.

Sources:

To build this component, I used several sources - however, as the result is kind of a mashup, I haven't included an licence information, as the code is all mixed up together. I used some of the structure of the existing Aura lightning component here. I also used some data structures and ideas from here.

UPDATE No more moment.js!! - It's uses the built in $A.LocalizationService object to do all date related tasks (which behind the scenes uses moment - but hey, I didn't load it!

Finally I was forced to use moment.js despite trying not to have any external dependencies, but due to a bug in the Lightning framework - I was forced to use it for string to date conversions.

Here's how to implement it:

Assuming you are using an Opportunity (obviously any object with a date would work), define the Opportunity as an attribute on your component:

<aura:attribute name="opportunity" type="Opportunity" 
                default="{ 'sobjectType': 'Opportunity',
                           'Name': 'New Opportunity',
                           'StageName': 'Some Stage' />

In your component, you need to handle the dateChangeEvent from the component:

<aura:handler name="dateChangeEvent" event="c:DateChange" action="{!c.handleDateChange}" />

In your form, put the below(once you have created it) as a top level member of the form:

<div class="slds-form-element slds-m-top--medium">
  <c:DatePicker aura:id="closeDate" label="Close Date" placeholder="Enter a Date" value="{!v.opportunity.CloseDate}" formatSpecifier="MM/dd/yyyy" />
</div>

Finally, in your controller or helper update your date:

handleDateChange: function(cmp, event, helper) {
  var dateSelector = event.getSource().getLocalId();
  if (dateSelector == 'closeDate'){
    var opp = cmp.get("v.opportunity");
    opp.CloseDate = event.getParam("value");
  }
}

How to use in a VF page - (once the component is built):

You will want a structure like this:

VF Page (instantiate and add callback)
       DatepickerWrapper (handle date change events, call callback)
                         Datepicker (perform date display and selection)

In your DatepickerWrapper component, handle the dateChangeEvent from the Datepicker and add a callback attribute (for lightning out):

<aura:handler name="dateChangeEvent" event="c:DateChange" action="{!c.handleDateChange}" />
<aura:attribute name="callback" type="String" description="Call this to communicate results to visualforce page" access="global"/>

Place the Datepicker in the DatepickerWrapper component like this (assuming you are using slds) (you may want to do all form element stuff in the parent vf page - up to you):

<div class="slds-form-element slds-m-top--medium">
  <c:DatePicker aura:id="closeDate" label="Close Date" placeholder="Enter a Date" value="{!v.opportunity.CloseDate}" formatSpecifier="MM/dd/yyyy" />
</div>

Instantiate the picker like this:

$Lightning.use("c:DatePickerApp", function() {
    $Lightning.createComponent(
        "c:DatePickerWrapper",
        {value : {!Opportunity.CloseDate, 
         callback: function(){
                     alert('callback');
                   }
        },
        "lightning",
        function(cmp) {});
});

Note the callback above - it's an attribute that will be called by the DatePickerWrapper class.

Finally, in your DatepickerWrapper controller or helper update your date by calling the callback on the vf page:

handleDateChange: function(cmp, event, helper) {
    var func = cmp.get('v.callback');
    if (func){
      func({fieldName:"CloseDate",value:event.getParam("value")});
    }
}

This is what it looks like:

Let me know if you find any bugs.