Watch the Single Note Picking online guitar lesson by Chris Buono from 60 Electric Guitar Techniques You MUST Know
The most basic approach to picking single notes is playing individual open or fretted notes with downstrokes only. When starting out, it's a good idea to explore different ways of holding a pick to see what works best for you. Experimenting with different picks is always an option, so don't think whatever you choose now is what you have to stick with. You can always change picks and, if necessary, even technique. That said, the latter is much more difficult, especially when you're trying to unlearn bad habits.
Some key factors in starting to establish a good picking technique are to always go with a firm, yet comfortable grip on the pick, angle your pick so less pick mass is making contact with the string, and try to pick more from the wrist then your elbow.
Looking for inspiration? Watch James Hetfield play. While you're at it, don't forget to consider most of the time he sings while playing.