Your app may be in the Apple's App Store, but there is still plenty you can do to improve your users' experience, as well as the app itself.
Good after sales support is as important as good code to the success of your app, never more so than in the period immediately following its initial release. Try to make as much use as possible of the resources at your disposal, including your support website and social media. The exact way in which you do this will vary hugely according to the nature of your app and the type of user you expect to be engaging with it.
Think twice, however, about making your site or social media pages open to comments from users. One disgruntled user can do a huge amount of damage, even while a thousand contented customers quietly use your app every day.
Direct feedback can, however, prove extremely useful in identifying the areas of your app that could use improvement, or that are not working as you intended them to. It is worth considering adding a feedback feature to the iPhone companion app (feedback from the watch itself is likely to find few takers, one would imagine).
In addition to feedback from your users, some analysis of how and when your app is being used could be critical at this phase. iTunes Connect now offers a considerable degree of analytical data about your app and you should most certainly take advantage of this free and constantly evolving source of information.
Two other popular candidates are also worthy of mention:
GA provides a free iOS framework that can be tailored to your app's needs and woven into its very fabric. You can set up GA to report particular events, window closures, engagement times and a thousand other things. The trick here is to decide what you actually need, and will profit from expending time on, both in including the code in your app (which is very simple but can become quite pervasive) and in reading through the data.
The documentation and download links can be found here:
https://developers.google.com/analytics/devguides/collection/ios/v3/
Another free framework, this one dedicated to crash reporting. If ten thousand users are using your app, you will be able to gain a very accurate picture of where any crashes are occurring, which will be a valuable aid in finding and fixing them.
If you choose to include this tool, here is where to start:
Basically, for post release, all these strategies are leveraging the fact that your app is now in active use, which can give you insights into its life among users that cannot be gained in any other way. It will cost a little time to include the code, and considerably more time to interpret the data, but some degree of analytics is probably appropriate to almost all mobile apps.