Your iPod shuffle is configured by default to force iTunes to automatically open when you plug it into your Mac or PC: this is a useful behavior, especially for new users, and in most cases. But, if you find yourself frequently plugging your iPod shuffle (and other i-devices like the iPad, iPhone, and other iPods), this can become an annoyance; fortunately, you can customize your iPod shuffle to prevent iTunes from automatically launching whenever you plug it in to recharge it, for example. This tutorial also explains how to access your iPod shuffle once you've customized iTunes not to launch for it.
First, connect your iPod shuffle to your computer; when iTunes opens, select the shuffle in the Sidebar on the left, and you'll see its "Summary" screen, which contains a series of settings (if it was already plugged in, make sure that the "Summary" tab is selected).
Scroll down you see the available "Options"; then, uncheck the "Open iTunes when this iPod is connected" checkbox. As soon as you do, an "Apply" button will appear in the lower right corner of the main iTunes window: click on it to save the new setting.
iTunes will take a few seconds to save and sync your iPod shuffle: once you see the "OK to disconnect" message, eject your iPod shuffle and unplug it, exit iTunes, wait a few seconds, and plug it back in. If you look at the shuffle while doing so, you'll notice that its LED light goes green for about a second, as visual feedback: you know that it is connected - and iTunes has not opened.
Now launch Windows Explorer or the Mac Finder, and you should (a) get confirmation that your iPod shuffle is indeed detected by your computer, and (b) be able to access its content outside of iTunes (assuming you also use your shuffle as a USB storage device).
If you want to manage your iPod shuffle from iTunes (adding or removing audio files and music, changing its settings, synchronizing podcasts, etc.), all you need to do is manually launch iTunes the way you typically do: as soon as it opens, iTunes will detect that an iPod is connected, and it will show it in the left Sidebar as usual! (And automatically start sync'ing it if you have left this setting to its default.)
Note: if you don't open iTunes while your shuffle is connected to your computer, eject it manually from Windows Explorer or the Mac Finder before unplugging it, as you would (or should!) with any external device. If you don't (or no longer) see your iPod shuffle in Explorer / Finder, launch iTunes and manually eject your shuffle from it. You will typically not have any issues if you accidentally unplug your iPod before ejecting it, but consistently doing so is the recipe for problems in the long run (though you might be able to repair corrupt-file-system-type issues from iTunes by restoring your iPod shuffle to "factory settings").
Quite intuitively, you can revert this behavior to its default at any point: just re-check the "Open iTunes when this iPod is connected" checkbox and click "Apply" - the next time you connect your shuffle to your computer, iTunes will automatically launch once again.