Windows Shortcut/Utility to switch between application windows
There actually is a way to do this and it's probably the most often-used keyboard shortcut in my arsenal.
Simply type Windows + number, where number is a single digit, 1, 2, 3, ..., 9, 0. This allows you to access the first 10 applications that are currently sitting in your taskbar.
For example, I have Chrome pinned to the 1st location in my taskbar, so Windows + 1 always brings up Chrome. My favorite text editor (Vim will never die!) is tied to Windows + 2. And on down the line. I have the first 10 locations in my taskbar pinned so that I always know what a given Windows + number combination will bring up.
But more to the point, since the OP asked how to switch between multiple windows of the same application, here's where this keyboard shortcut gets really useful. To refine what I said earlier, Windows + number brings up the first instance of the application. But holding the Windows key brings up a list of windows of that application. (Similar to when you mouse over the grouped icons of an application in the taskbar.) Continuing to type Windows + number scrolls through that list.
For example, I earlier said I have Chrome tied to Windows + 1. More specifically, I always make sure that my gmail and calendar are in the first window of Chrome, so that Windows + 1 always jumps right to my email. But if I want to cycle through any of my other Chrome windows, I just keep the Windows pressed down and keep typing Windows + 1.
Another related and particularly useful variation of this is to add the Ctrl key. Windows + Ctrl + number brings up the last active window of the given application. This is very useful when you keep toggling back and forth between two different windows of the same application.
UPDATE Jan/2019: The above Windows + Ctrl + number shortcut appears to have been removed in Windows 10, starting from either version 1803 or 1809. I'll update this answer if I figure out a way to re-enable this shortcut. See https://superuser.com/a/1388225/288800, where there seems to be consensus that this is a bug, not a feature removal. Hopefully that answer will contain useful information if I forget to come back and update this one.
Please note that this answer was originally written when I was using Windows 7, but these shortcuts are also applicable according to Windows 8 and 10. See https://support.microsoft.com/en-us/help/12445/windows-keyboard-shortcuts for an explanation of the shortcuts in all three of those versions of Windows. That link also explains Shift and Alt key variations which you may also find useful, so I recommend taking a look at it.
UPDATE Nov/2019: Microsoft appears to have restored the Windows + Ctrl + number shortcut in Windows 10 version 1903. Hooray!
There's no built-in way to switch between the windows of the same application. All top-level windows are displayed in Alt + Tab list. I mean if you have two instances of Notepad running, you'll see two windows of Notepad in Alt + Tab window list.
If you activate two windows of the same application in row, you can switch between them with single Alt + Tab press.
Additionally you can press Alt + Ctrl + Tab to display the list of windows, and then use arrow keys to select the required window; press Enter to switch to the window.
You can also use mouse to select a window from this list.
As an alternative way you can use Windows + T: each press activates the next button on the Taskbar (including the pinned, not started, applications). When you reach the required application, press Enter or Up and then use Left and Right arrows to select the required window and press Enter to switch to it.
Definitely Windows + T is slower than Alt + Tab.