I never had MobileMe, but I have used the sharing feature in iCloud. The official name is called "Shared Photo Streams". It will only be viewable by someone running iOS 6 or later and the latest version of iPhoto (it may work on PC, but not sure).
Set up on Mac:
1) Open iPhoto
2) On the left toolbar, select "Photos"
3) Select all the photos you want to share
4) Select "Share" at the bottom left of the window
5) Click Photo Stream
6) Here you can add them to an existing Photo Stream or create a new one
For a new one, just finish following the on screen instructions
Set up on iOS device (requires 6.0 or later):
1) Go to the Photos app
2) Select "Photos" from the toolbar at the top
3) Click "Edit" at the top right
4) Select the photos you wish to share
5) Click "Share"
6) Click "Photo Stream"
7) Here you can add the selected photos to an existing Photo Stream or create a new one.
For a new one, follow the rest of the on screen instructions