iCloud requires you to have 10.7 or 10.8 on your computer. iCloud system requirements - http://support.apple.com/kb/HT4759. Note that "photo stream" requires iPhoto 11.
iCloud set up - http://www.apple.com/icloud/setup/.
on your computer - Click the apple / system preferences / iCloud - sign in with your iCloud Apple ID
If you have iPhoto 11, click the word "iPhoto" beside the apple and select "preferences", then go to the "photo stream" tab. Enable photo stream.