I prescribe to Malcolm Gladwell's method of preparation [1] in that I write out every single word of my talks beforehand and more-or-less memorize them. It's not my explicit goal to memorize every word, but I go over the words enough that that's essentially what happens. I actually end up memorizing key sentences and phrases more than words. Even moments that I seemingly "ad-lib" to the audience -- jokes, side comments, "random" anecdotes -- are written out beforehand. That way when I'm in the moment I can focus on delivery and not content.
I think the biggest driver to my anxiety of public speaking was the possibility of sounding stupid, but as long as I have the confidence that I've written out a good argument beforehand then that goes out the window. I stick to the script because I know the script will work.
As far as mentality goes, there is no better feeling than looking out into an audience of people and see them staring back at you, listening to every word. No smartphones out and no sleeping, just attention. While I still get a little nervous, it's nowhere near what it once was, and I actually look forward to connecting with those whom I've been invited to speak with. My excitement for that connection has started to trump my nerves.
Clearly I'm not in the camp of "don't prepare and just go wing it, it'll be more natural" because it really opens up the door for panic-induced disaster. And I really hate sitting in a talk that the speaker is clearly unprepared for. It's unprofessional and disrespectful. If people are going to give you the respect of their undivided attention, give them the respect of real preparation.
[1] http://www.thepowerofintroverts.com/2011/01/26/public-speaki...