Transfer apps to my new iPhone?

Follow the directions here:

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

I just bought a new 5s and backed up my 4s to the cloud as the link points.

When restoring from the icloud backup, will it also restore the game saves and app documents or only the apps themselves?

iCloud will restore all your iPhone 4s apps including its app data (game saves). If you are after transferring individual apps and their app data to your new iPhone, also look at this: How to transfer iPhone apps to another iPhone, iPad or iPod Touch