When you wish to allow access to a SkyDrive photo album to everyone and anyone on the Internet the share setting needs to be set to Everyone. When you create a new folder of album the sharing will be set to 
“This folder is not shared”.
To share the folder click the Share folder link.
This brings up a dialog where you can specify email addresses and other specific ways to share. To make the album public click Get a link.
This next dialog has a Make public button.
Click the Make public button.
The folder is now public. You will see a text box with a length URL. 
You can copy this web address and share it with your friends. There is also a Shorten button. Clicking that provides you with a shorter web address.
The information pane will now show that the folder is shared with Everyone. There is an X to the right of this setting, the normal “delete” icon. Click that to remove the permission.
You can use the web address in emails to your friends or in blog posts and wherever you wish to provide a link to your SkyDrive photo album. Viewers do not need to sign in to see public albums.
.:.
© 2012 Ludwig Keck
Ask Ludwig 
That was just what I was looking for. Many thanks!
I use this for my students and asked them to bookmark the link. But when they try to use the bookmark they cannot get acces without signing in to SkyDrive. But if they reuse the original link there is no problem in accesing it. How do I (and my students) bookmark or use the bookmark?
Bonusinfo: it is a OneNote file that the students are suppose to follow in class to see notes I write.
Hope you can help.
Ah, the delights of SkyDrive security! Here is a quick workaround: First get a short URL for the notebook (Share > Get a link > View and edit > Shorten). Copy the link and provide it to your students. Have them bookmark the page when using it the first time. NOW THE TRICK: Have them edit the bookmark and replace yhe URL the browser captured with the short link. I have tried it in several browsers, this works fine. I will share this trick in a post. Thanks for asking!
doesn’t seem to work anymore.No matter what I try, a MS account sign in is required.
Thank you jakemono for sharing the new problem. I have not yet replicated this problem.
no matter what I seem to need an MS login now. Any suggestions?
The latest changes to SkyDrive sharing and security seem to cause some weird problems. I will try to figure this out and post my findings.