To obtain the magnetic stripe data from your card, you will need a reader. In the US, they are available on both Amazon and Ebay for around $20 delivered. The inexpensive ones are USB devices that act as keyboard input, so no special drivers are needed on Windows or Mac OS X computers. While I’m sure there’s more secure options, you can use an app like Google Keep or Docs to quickly transfer the swipe input to your phone and paste it into the app. The card data entered into the app is stored using Android’s SharedPreference API in a way that is not accessible by other apps on a non-rooted phone.
The full source code to SwipeYours is available on Github: https://github.com/dimalinux/SwipeYours
Blog describing many details of SwipeYours: http://blog.simplytapp.com/2014/01/host-card-emulation-series-swipeyours.html
SwipeYours requires both NFC and and Android version >= 4.4 for HCE (Host Card Emulation).
Privacy: This app has no Internet permissions and will not transfer your card information anywhere other than over the NFC interface for payments.