Async methods go something like this:
Flickr f = new Flickr(ApiKey, SharedSecret, AuthToken);
// check r.Error to see what the error is.
// r.Result is the actual result.
PhotosetCollection photosets = r.Result;
r is an FlickrResult<T> where T will be the actual result for whatever you are calling (in this instance FlickrResult<PhotosetCollection>).
If you didn't want to use lambda expressions you could create a method that took the FlickrResult<T> as an argument like so:
private void PhotosetGetListCallback(FlickrResult<PhotosetCollection> r)
// check r.Error and r.Result in here.
// and then call as follows:
var action = new Action<FlickrResult<PhotosetCollection>>(PhotosetGetListCallback);
Sorry for the delay in replying. Hope that helps.