I personally think the best library right now would be fmdb, wrapped around sqlite:
https://github.com/ccgus/fmdb
This is probably one of the more mature libraries, and isn't too bad to get used to if you are familiar working in other frameworks.
Previously, database apps were kind of hacked, you'd dump data into a Json file, and another language like php would pick up that data and push to a database using normal methods. An example of this was taught here:
http://codewithchris.com/iphone-app-connect-to-mysql-database/
I've used similar methods for desktop apps, but now other libraries are being designed to serve this purpose. Here's one that actually does pretty well, even though it's meant for mobile use specifically, can be used for desktop use as well:
https://realm.io/docs/swift/latest/
A lot of these are still very young and have yet to mature into something that is usable long term, but is enough to get started with.