I'm afraid Snow Leopard is not compatible with iCloud - the minumum requirement is Lion 10.7.2. This is the situation with Snow Leopard and existing iCloud accounts:
- You will be able to access email and calendars on the iCloud website at http://icloud.com provided your browser is reasonably up-to-date.
- You will not be able to sync contacts or bookmarks from a pre-Lion Mac.
- You will be able to enter the server settings for email manually in the Mail application and access your email.
- You will not be able to sync your calendars directly.
- Some people have been able to set up calendar syncing by using the method detailed here - this is an unsupported hack and may not be reliable, and may stop working at some future point.
- Address Book won't sync: this page has a convoluted hack to make it sync which has been reported as working (and as not working by others). I've not tried it.
Although it's not a cheap solution, Soho Organizer can sync Calendars and Contacts with iCloud on Leopard, Snow Leopard and Lion. A single user licence (multiple machines allowed) is $99.99. (I have no connection with this firm.)