How to download video from url and save it in to document directory in iOS
You can use the NSURLConnection method sendAsynchronousRequest:queue:completionHandler:
.
That one method will download an entire file into an NSData object and call your completion handler method once it's done.
If you can write a app that requires iOS 7 or later, you could also use the new NSURLSession
API. That offers a lot more features.
If you search using those terms you should be able to find tutorials and sample apps illustrating both APIs.