I am writing a keyboard extension in Swift right now and highly recommend not doing the same. Both Swift and the Keyboard Extension API are brand new, not well documented, creating significant learning curves, and both have significant bugs or weird implementation details to work around.
From the way you phrased your question it doesn't sound like you are very experienced in iOS development, and attempting to learn too many things at once is a recipe for disaster. If I could do my current project over, I would have done it in Objective C just to vastly simplify what I was learning.
But the good news is that you don't need the keyboard to run in other apps. This is good news because writing a custom input keyboard class within your own app is very simple and easy, and a great place to start. There is a good deal of existing documentation on how to do so, including this excellent post on stack overflow.
How do I retrieve keystrokes from a custom keyboard on an iOS app?
More detail:
The standard custom input view API in cocoa is very powerful, the one in the keyboard extension is almost entirely neutered, so you can do far more with a custom input view than you can with a keyboard Extension. To activate a keyboard extension requires getting the user to turn it on in their iPhone settings, there is no way around that and no way to pick which keyboard they choose within your app (other than to not allow custom keyboard extensions at all).
If you need to access the internet or data within your app for any reason (tracking usage information, activating an in-app purchase, accessing preferences) you must also convince your user to turn on "Full Access", which presents an incredibly scary alert that reads to users as if turning it on means you will be able to spy on them and steal their passwords
Getting back to why you don't want to use Swift in an extension. First, Objective C doesn't cause Xcode's code parser to crash many times a day, while developing in Swift does, sometimes crashing Xcode itself. In Objective C the debugger is almost always correct, in the current version of Swift often you can't see array or dictionary contents, sometimes what it shows is inaccurate, and when stepping through code often takes nonsensical routes. Developing in Objective Code means you won't have to update your code because of changes to Objective C itself, with Swift it's pretty much guaranteed they'll make significant syntax changes every major release (the last one in September did).
Developing a keyboard extension means sometimes your extension won't load for mysterious reasons, and you'll need to waste hours debugging why. My Swift keyboard extension is sometimes debugged solely with println() statements because I can't get the debugger to load. Since Apple's tools don't yet work well with Keyboard extensions, and also don't yet work well with Swift, using them together are multiplying your pain exponentially.
The end result is if you don't need to use this keyboard outside of your own application it's foolish to build it using the Keyboard extension API. If you do need to use the Keyboard extension API it's foolish to do it in Swift. This is written by a fool working full time trying to ship a Swift based keyboard extension.
If you want to use the standard cocoa custom input view API, then using Swift is probably fine. You will still have to deal with additional problems because it's such a young language, but you won't have lose so many days to mysterious, seemingly insoluble problems trying to figure out if they were caused by Swift, the Keyboard Extension API, failures in Xcode and it's debugger, or your own blunder.
