Find some photos that you want to add to the Shared Stream, then tap the Select button and select the photos you wish to add.
With some photos selected, tap the Share button and select i Cloud from the Share Sheet.
After this, you can then specify if you'd like to invite any i Cloud users to subscribe to it.
While it's not immediately obvious, you can simply tap Create without entering any details if you'd prefer to send out invites later on.
To manage the Shared Stream, such as invite new subscribers or make it accessible via the web, click the Info button within i Photo.