When Microsoft overhauled Office Online recently, a number of users noticed that the Office on Demand option was no longer available. But after checking with Microsoft, I discovered that this feature is still available. It's just not promoted explicitly anymore in the consumer versions of the Office online services.
Before we jump in, a quick explanation.
Office on Demand is a feature of the new Office wave of products that lets you "stream" individual Office applications—like Word, Excel, PowerPoint and so on—down to a PC that does not have Office installed. You can then use those Office applications as if they were installed locally. When you're done using them, and close them, they are removed from the PC and it's like they were never there.
Before the recent Office.com overhaul, Microsoft offered explicit access to Office on Demand from the same page that you used to download the Office software. But with the overhaul, the whole site was redesigned and now that option is gone.
Note: These instructions apply to OneDrive (the consumer version) and Office 365 Home Premium, not the business versions of Office 365. If you're using an Office 365 subscription for businesses, you will still see a "Use Office on Demand" link in OneDrive for Business on the web. So it works as it did previously.
As it turns out, you can still use Office on Demand. Just sign-in to OneDrive (or select OneDrive in Office.com), navigate to the document you'd like to open, select it, and then select "Open" and then "Open in Word" from the menu bar. (Or, right-click the document select "Open in Word.")
Obviously, if you have Office installed on the PC, the correct Office application will launch and open that document. If you don't, however, you'll be prompted to "stream and use your subscription." This will require a browser plug-in, if you've not done this before, and a quick local install of Office on Demand. Then, the correct Office application will begin streaming—it's smart, so it will load the bits you need first—and you'll be prompted to sign-in to your account so you can begin editing. (The application will even be configured with whatever custom settings you're syncing through OneDrive.) The whole process takes about a minute.
Here's a sequence of shots showing how this works.