As described in an earlier blog post SharePoint Online comes with a very useful template "Express Team Site", from which you can easily fire up Office documents by clicking the built in icons (see below). Default behavior is that the document opens in the Office rich client if such is installed on the PC. If no Office is installed on the PC, the document will open up in Office Web Apps.
Some of you are perhaps wondering if you can in fact force the latter - make the documents open up in Office Web Apps no matter what. It can be done by disabling an add-on in IE (see how to further down in this blog post).
If you disable this add-on the behavior will change as follows:
1. Open your Express Team Site, and click e.g. the Word icon
2. Now instead of being taken to the Word rich app installed on the PC, you remain in the browser and are prompted for a file name
3. After typing in a document name and clicking OK, Word Web Apps opens
4. After saving and closing you are back in the doc lib.
Here is how to obtain the above
1. Open IE and click "Manage add-ons" in the "Tools" menu
2. Click "All add-ons" (lower left corner)
3. Locate the "SharePoint OpenDocuments Class" add-on and disable it
Thats it. Thanks to Ryan Phillips for hinting.