If you have a tilde in your path you can try this:
let location = "~/file.txt".stringByExpandingTildeInPath
let fileContent = NSString(contentsOfFile: location, encoding: NSUTF8StringEncoding, error: nil)
otherwise just use this:
let location = "/Users/you/Desktop/test.txt"
let fileContent = NSString(contentsOfFile: location, encoding: NSUTF8StringEncoding, error: nil)
This gives you a string representation of the file, which I assumed is what you want.
You can use NSData(contentsOfFile: location) to get a binary representation, but you would normally do that for, say, music files and not a text file.
Update: With Xcode 7 and Swift 2 this doesn’t work anymore. You can now use
let location = NSString(string:"~/file.txt").stringByExpandingTildeInPath
let fileContent = try? NSString(contentsOfFile: location, encoding: NSUTF8StringEncoding)