Drag and drop with Finder to an external storage device. This will work for your documents, pics, etc...
As far as apps, you can try drag and drop, depending on the app it may work. If the app is an OS X Yosemite specific version it probably won't work, and apps with dedicated installers(.pkg files for installation) might not work this way either. If some of the apps that are missing were installed using the App Store, just login to your Apple ID on the Mac with Mavericks and redownload those apps.