Getting a new iPhone 5 and handing down my old 4S
Back up the 4S (either to your computer or iCloud), then when you set up the 5, select to restore from the old 4S backup. That will restore your iCloud account, and all apps and content.

Once the 5 has been successfully set up with your content, wipe the 4s (Settings → Reset → Erase All Content and Settings) and set it up from scratch, with a new iCloud account for your wife (unless she has an existing one).

It's important to note that your phone account is tied to the SIM card in the phone, so calls and SMSes sent to your existing number will still go to the iPhone 4S, and the iPhone 5 will be linked to your wife's account. To change this, you need to swap the SIM cards, which is easy to do, except the iPhone 4S uses a micro-SIM, whereas the 5 uses a nano-SIM. You're likely going to need to talk with your phone provider to reprogram the SIMs, or get new ones of the proper sizes.