Have been notified by phone call, email, FedEx, UPS, USPS of big wins. Also have been notified immediately on screen (Instant Win) of a very big win.
The most common way is by email. I've only been called 3 times for wins, 2 of them large wins, 1 of them a smaller win.
I answered all 3 of my phone call wins, so in those instances, not sure if they would have left a message. I believe the rules for one of them stated they wouldn't leave a message, but would try twice in a small time period, and if no answer would move on to next person drawn. I answered, thankfully. Watch the rules and there is usually a section about winner notification. Some sweeps will go into details about how they notify winners, others don't.
I know phone notifications can be an issue for lots of folks, luckily that's not the most common way to be notified (in my experience). I use my cell phone for sweeps entries, and since I always have it on me and can answer it at any time, I haven't missed anything yet (that I'm aware of!).
Hope that helps, and hope you get some really nice wins!!!
Jeff
$10,000 Club member since November 2008!