How do I transfer my photos, contacts and apps from my iphone 4 to iphone 4S?

Sync your iPhone 4S in the computer that you use to sync your iPhone 4 and everything will migrate to your new phone. With contacts and photos taken in your iPhone 4, you can use iCloud

Disable "auto-sync" in iTunes first. Preferences - Devices - Prevent iPhone/iPod from automatic syncing.

To be on the safe side, import all of the photos/videos (Camera Roll) from your current iPhone to your computer.

http://support.apple.com/kb/HT4083

Backup your contacts on a compatible programme on your computer (Outlook, Address Book, Windows Contacts etc) or in iCloud.

Now follow the steps mentioned in this article.

http://support.apple.com/kb/HT2109

Later, sync the contacts with your new iPhone from the programme/iCloud you used to back them up.

Sync your contacts to an address book app on your computer from your old phone, then sync the new phone to the same app. "Sync" is just that; it is not an overwrite.

You may transfer the data from your iPhone4 to iPhone4S by using iTunes or iCloud. If you choose to use iCloud, you may:

Back up the old iPhone manually with iCloud by opening “Settings, tap “iCloud”, navigate to bottom and tap on “Storage & Backup”, then tap “Back Up Now”

Boot the iPhone 5 and walk through the easy setup, choose either “Restore from iCloud Backup”

Wait until the new iPhone restores from your old iPhone backup, this can take a while depending on the size of your backup, how much stuff you have on the iPhones, and the speed of your internet connection

When finished, your new iPhone will have everything from the old iPhone and you’re ready to go!

To transfer data from one iPhone to another:
1. Connect two Devices to PC.
2. Choose the category list of one device that you need to export files
3. Check the files that need to export in the Content Panel and click "Transfer file(s) from device to device" button
4. All the checked files from one device can be transferred to the other one.

The easiest method is via backing up the old iPhone with iCloud. Then restoring the iCloud backup to the new iPhone - this will restore contacts, messages, camera-roll photos, apps and app data.