How do I sync an iPhone 4s to an Imac that's running Tiger OSx 10.4.11?

Not possible. Syncing an iDevice requires a minimum of Snow Leopard 10.6.8 on an Intel Mac.

Syncing an iPhone 4S with a Mac requires Mac OS X 10.5.8 if the device is running iOS 5 or 6 and Mac OS X 10.6.8 if it's using iOS 7.

Choose About this Mac from the Apple menu and check the processor.

If it's a G3, no further OS upgrades are available.

If it's a G4 or G5 and the iOS device is running an OS version prior to 7.0, buy a retail Mac OS X 10.5 DVD from a source such as Amazon or eBay; Apple still might have copies in stock if you phone them.

If it's an Intel Mac, buy a Mac OS X 10.6 DVD from the online Apple Store.

Back up your data before upgrading.

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A simple and popular way to copy files and share files among your devices.

https://www.dropbox.com/

"Box lets you store all of your content online, so you can access, manage and share it from anywhere. Integrate Box with Google Apps and Salesforce and access Box on mobile devices" Rated the most secure cloud storage by SkyHigh Networks.

https://www.box.com/

Using iTunes to transfer files:

http://support.apple.com/kb/HT4094?viewlocale=en_US&locale=en_US

Files Connect -- "Cloud Storage services like Dropbox, MobileMe iDisk, Google Docs/Picasa, Facebook photos, FTP, SFTP, WebDAV ... AFS (Apple File Shares) SMB (Windows shares) protocols"

https://itunes.apple.com/us/app/files-connect/id404324302?mt=8

"The kiteworks mobile file sharing solution provides secure creation, viewing, and sharing of enterprise content on smartphones and tablets while providing IT and security teams the administrative controls to manage user privileges and access rights necessary to ensure enterprise security and compliance." " Includes choice of private cloud on-premise."

http://www.accellion.com/solutions/mobile-enablement/mobile-file-sharing

"Dukto is a simple application that allows you to share files between devices connected to the same (wireless) LAN network."

http://www.tidal.it/?page_id=309&lang=en

http://www.msec.it/blog/?page_id=11