#1
I want to play "Everybody Wants to Rule the World" by Tears for Fears and my favorite part is the intro. I have only been playing since late July, but I feel as if the correct technique for that part of the song is alternate picking. I have two questions:
  1. Is that the right technique?
  2. How do I alternate pick without too many hiccups in my playing?

Thank you!
#2
A lot of times on guitar, there isn't going to be a "right" or "wrong" technique per se. For a particular lick or riff, you could down pick, alternate pick, economy pick, hybrid pick, use all down strokes, etc. It's really a matter of what is easier and what sounds right to you. It's good to learn to play different parts in a variety of ways to see what you like best.

As for your second question, it's just practice. You practice and practice until you have the technique down. Once you have it down you don't really think about it. That's kind of the goal really -- getting things to the point where you don't really need to think about them.
There's no such thing; there never was. Where I am going you cannot follow me now.