Well first of all, if you're going to be playing melodies, not just riffs/rythm, alternate picking is essential, so get on it immediately. When you start, make sure that each pickstroke alternates, always. Never repeat downstrokes or upstrokes. Later on, you may want to experiment with this, or you may not, but it's good to be able to do standard alternate picking first.
There's not really a secret to it, and there's no way I can make sure that you won't do it wrong, so I suggest you get somebody who plays well to watch you. The best would be to get a teacher, are you taking lessons? A good way to improve your picking is to play stuff that is incredibly easy for the left hand or doesn't even use the left hand. Practice alternate picking on one string, practice alternate picking crossing strings. You can do this with scales too, but if you want to concentrate on developing picking ability, it's not necessary. Later on, you will definitely want to include your left hand in picking excercises, however.