Although I'm only focusing on the Windows 8 / Windows Phone 8 family in this post, you should also be aware that Microsoft has SkyDrive apps for other device platforms including iOS and Android.
A number of these techniques can be used for any kind of file, but the most widespread SkyDrive support across Windows 8 and Windows Phone 8 appears to be for photos and documents. Since you can have Office on any of these Windows-family devices (your PC, your tablet, your phone), being able to have a central place for documents, worksheets, and presentations you can get at from whichever device you happen to be using is pretty awesome.
SkyDrive Windows 8 Application (Windows 8, Windows RT)
The most obvious way to take advantage of SkyDrive on Windows 8 or Windows RT is to notice the app named "SkyDrive" on the start screen. This will let you get to and work on your SkyDrive folders, but the app does not appear to have any features for moving content between your local device and SkyDrive folders as far as I can tell. Actions the app makes easy are browsing your folders, opening an image or document, or uploading files from your local device to a SkyDrive folder.
SkyDrive App Included with Windows8 or Windows RT (Start Screen)
SkyDrive App - Folder View
SkyDrive App - Images in Folder
SkyDrive App - Spreadsheet in Folder
App Storage - Auto-Integration with File Save / Open Dialogs (Windows 8, Windows RT)
One very automatic integration with SkyDrive is that when a Windows Store App presents an open file or save file dialog, the areas you can navigate to (Documents, Pictures, etc.) include SkyDrive.
SkyDrive Built-in Open and Save As Dialogs
SkyDrive Folder on Your Windows 8 PC (Windows 8 only)
x86 devices that run Windows 8 or Windows 8 Pro also have the classic desktop and can run Windows 7 type apps. A tip from Paul Thurrott's Windows site points out you can have a Windows Explorer-style experience on your classic desktop by downloading the SkyDrive Windows Desktop app from the SkyDrive site (note, this app is also included in Windows Essentials 2012). Here's what the SkyDrive Windows app looks like on my Dell Laptop running Windows 8 :
SkyDrive Folder Explorer on Windows 8 - Folders View
SkyDrive Folder Explorer on Windows 8 - Image Files in Folder
SkyDrive Folder Explorer on Windows 8 - Spreadsheet in Folder
The previous tip is fine on x86 devices like a laptop or tablet PC, but it won't help you on a Windows RT ARM device (for example, on a Microsoft Surface RT). But there is still a way to get an Explorer-style view: you can map your SkyDrive root folder as a mapped network drive. Even though Windows RT can't run your classic PC apps, it does in fact still have a classic desktop (Windows + D will get you there) which includes Windows Explorer. You can map your SkyDrive folders to a drive letter by following the procedure described on Rashed Talukder's blog.
Mapping SkyDrive to a Local Drive Letter
Accessing SkyDrive on Microsoft Surface on Windows RT Desktop
SkyDrive on Windows Phone 8
Microsoft has a SkyDrive app in the Windows Phone store, and it's free. With it, you can browse your SkyDrive folders and files and open them (for example, opening a worksheet in Excel). You can also upload photos from your phone to your SkyDrive storage. Here's what the experience looks like on my Lumia 920 Windows 8 phone:
SkyDrive: An Essential Companion for All Your Devices
We've looked at quite a few different ways to incorporate SkyDrive into your devices. Note that when you update your files in a SkyDrive folder, some of the methods above will auto-detect the new content while others have a Refresh button.
All of this makes for an extremely easy and versatile way to share data across devices that can access SkyDrive--with all these options, you can choose the approach that best fits what you need to do and the device/OS you are using. I particularly like the universal access this gives me to my Office documents.
Since I'm just starting to play with this, I'm sure there is plenty more you can do with SkyDrive on Windows 8 and Windows Phone 8. I'm also hoping to find a way to sync SkyDrive folders to local folders automatically, so I can get to my stuff even when offline.
As a Windows Azure guy, I haven't paid all that much attention to SkyDrive until recently--but as you can see, it's become quite capable and broadly accessible. I'll post more tips as I come across them, and please send comments if you have some to suggest.