As of July 2013, Instagram has not released an iOS app optimized for use on the iPad or iPad mini. The iPhone app can be used on these larger devices, though the program interface will not elegantly fit the iPad mini's interface. Alternatively, you can use the Instagram website to access some of the service's functions or switch to a third-party app to access Instagram on your iPad mini instead.
Instagram's iOS app
The official Instagram app for iOS devices is free to download and use (see Resources), and it is compatible with all devices running iOS 5.0 or later. The app enables you to browse through the feed of users you're following and post photos and videos of your own, complete with any filters, people and place tags you want to associate with them. Various account settings can be managed from the app as well, including the information displayed on your profile and the people you're currently following.
Running Instagram on an iPad mini
Search for "Instagram" through the App Store app on an iPad mini. You'll need to switch to the "iPhone Apps" tab of the results page to see the Instagram entry. The official Instagram app lists "Burbn, Inc." as its developer. Once the app is downloaded and installed, you can log in with your account details to use Instagram. As with all apps developed solely for the iPhone but running on an iPad, you have the option to run Instagram at its original size or at twice the original size (tap the "2x" button to do this). You can browse through photos from your friends, add likes and comments, upload photos of your own and manage your profile from within the Instagram app.
Instagram on the Web
Certain Instagram functions, as well as a profile page showing off some of your pictures, can be accessed through the Instagram website on the iPad mini's browser. Launch the Safari app (or another browser app of your choice), head to the Instagram website and log in using your account credentials (see Resources.) From the site you can view photos from your stream as well as your friends' streams, add likes and comments and edit parts of your profile. As is the case when accessing the Instagram site through a desktop Web browser, you cannot upload new photos through the online interface.
Instagram for the iPad
Instagram has made no announcements regarding the future release of an iPad-optimized app for the service. As Instagram offers an API (Application Programming Interface) through which other apps can connect to the service. Various third-party tools are available for Instagram on the iPad, including InstaFlow, Padgram, Pictacular, Iris, InstaPad, Instagallery and Instamap. Depending on the type of features you use most on Instagram and how much you're willing to pay, you may prefer using one of these apps to the official Instagram one. However, bear in mind that these apps are not officially supported or approved by Instagram itself.