You can see a detailed example of how to make HTTP calls (GET, POST, etc..) in swift here.
From the link above,
You can use NSURL, NSURLRequest and NSURLSession or NSURLConnection as you'd normally do in Objective-C. Note that for iOS 7.0 and later, NSURLSession is preferred.
Using NSURLSession
Initialize an NSURL object and an NSURLSessionDataTask from NSURLSession. Then run the task with resume().
var url = NSURL(string: "http://www.stackoverflow.com")
let task = NSURLSession.sharedSession().dataTaskWithURL(url) {(data, response, error) in
    println(NSString(data: data, encoding: NSUTF8StringEncoding))
}
task.resume()
For more detail, check the documentation for the NSURLConnectionDataDelegate protocol