All Tim's advice is great here. Just wanted to add: keep your pick perpendicular to (pointing towards) the front of the guitar, so it isn't pointing even slightly upwards or downwards. Often beginners get used to playing down-picks first, and having their pick pointing slightly upwards. This often causes the pick to get caught under the string on up-picks.
EDIT: Hey everyone! Just to be clear, Dougus and I might be talking about DIFFERENT pick 'angles'. I think he's talking about turning the pick slightly in relation to the string; as he says, this allows it to glide off the string. This is the same way classical guitarists use their nails to release the string (usually described as creating a ramp to release the string). This can work well with a pick, but it will affect the tone. Generally your sound has more attack, and so a brighter sound, if you keep it in line with the string, and you get a mellower sound if you turn the pick a little. Also, if you want to play really fast don't turn the pick too much, as the pick has to travel further on each note as it glides over the string.
Anyway, the pick 'angle' I'm describing in my answer above, is the direction of the pointy end of the pick. You want this to be at 90 degrees to the front of the guitar's body. This means that you will be able to pick the same for up-strokes and down-strokes, which will help you to play fast and fluently.
When I describe pick position to my pupils, I compare it to flying a plane, as though the pick is 'flying' towards the guitar. The pick position can be changed in three ways: 1. whether the end of the pick points up or down, this is like the 'pitch' when flying a plane (front of the plane pointing up or down); 2. whether the end of the pick is turned in relation to the string, this is described as 'roll' when flying a plane; 3. whether the end of the pick points sideways (towards the neck or your right elbow), this is like 'yaw' when flying.
As with so many aspects of guitar playing, this can be demonstrated face-to-face in seconds, but is a little harder to describe in text!