If you're looking to only pass the image as part of the request body, this is pretty easy to do.
In iOS, you would set the request.HTTPBody = <your data here> and in ASP, you could read the body using Request.BinaryRead(Request.TotalBytes). For performance reasons you would probably want to break up the binary read into smaller parts of the file, but that's basic file parsing.
If you want to pass additional parameters, you will need a bit more work since neither NSURLRequest nor classic ASP have a native understanding of multipart requests. You're on the right track with the file upload class, as it will handle multipart on the server side. For the client, I recommend using a framework like AFNetworking. From their FAQ, you can do something like this:
NSData *imageData = UIImagePNGRepresentation(image);
NSURLRequest *request = [client multipartFormRequestWithMethod:@"POST"
path:@"/upload" parameters:nil
constructingBodyWithBlock:^(id <AFMultipartFormData> formData) {
[formData appendPartWithFileData:imageData name:@"avatar"
fileName:@"avatar.png" mimeType:@"image/png"];
}];