You cannot do that. Photo stream is not meant as a way to share your photos with others. It is meant for one person to share the photos with their multiple devices. You need to use a personal web site or one of the many photo sharing web applications where you upload your photos to share. Many people now use Facebook to share photos with friends and family.
Message was edited by: bobwild
according to bobwild, it is not possible to use Photo Stream to share on the web. However at this page http://www.apple.com/icloud/features/photo-stream.html, we see the following quote "If the folks you’re sharing with are using iCloud on an iOS 6 device or a Mac running Mountain Lion, they’ll get a notification to view your pictures right in the Photos app or iPhoto. If not, they can view your photos on the web." as well as a screenshot of a person viewing photos at a URL like http://photos.icloud.com/share/xyz.
This cnet page http://howto.cnet.com/8301-11310_39-57508640-285/how-to-create-a-shared-photo-st ream-album-on-ios-6/ also mentions it: "If you want people without an iCloud account to be able to view the album on the iCloud Web site, toggle the Public Website switch to On."
Of course we should also mention that in iPhoto, the sharing panel has a checkbox which reads: "Public Website. Allow anyone without an Apple device to view this Photo Stream on a public website."
And on the iPhone the sharing pane has a toggle switch which reads "Public Website. Allow anyone to view this shared photo stream on iCloud.com"
However, I have tried sharing via iPhone and iPhoto, with the public switch turned on, and neither I nor the recipient of my sharing request see any photos on iCloud.com, and going to photos.icloud.com gives a connection error.
What is going on here? If no such functionality is supported, why does the documentation and the software itself pretend it is?
In Photos, click the Photo Stream tab. On that page, it will show your photos in your p. stream (teehee), and it will show your Shared Photo Stream collections. Do not open the collection, but rather click EDIT in the top right corner of the Photostream tab.
And then click whichever Shared Photo Stream you want the web link for. A pop up window titled "Edit Photo Stream" will rise up.
In that window, you can change the Shared Photo Streams name, add people to the "Subscribe" list (those that have iOS or iPhoto or Photo Stream on their windows machine), and then the on/off switch for the public website where you get the link to share with those that don't have an iDevice or iCloud account. It will show you the link address if you have Public Website enabled and the option to share that link right above it.
I was banging my head over this same problem, and it was a matter of looking and finding it in a place that isn't very intuitive. I came across it by luck. I started browing the boards to find the answer JUST as I found the answer! Hope that helps, unless you already figured it out.