Downstrokes are easy! Why? Because you have gravity on your side - the motion of the lower arm falling with no muscular tension allows your strumming hand to automatically follow through the strings at the correct angle of attack (pick tip angled up).
The problem with upstrokes is that the change in direction of the lower arm necessitates a certain amount of muscular tension in order to get the arm moving in the opposite direction. The trick is to use just enough muscle power to get the arm moving back up without locking up the wrist, your wrist must remain supple and free throughout the whole strumming motion. Providing your strumming arm and hand remain tension free on the way back up, then your pick should automatically follow through the strings at the correct angle of attack (pick tip angled down).
Here's a way of getting an idea of the motion that you need to achieve. Imagine that you have piece of tape stuck to your finger tip and you want to flick it off. Your natural instinct is to flick your wrist up and down to dislodge it, however this movment introduces tension in your lower arm as you are using muscle power to move the wrist. Now try to dislodge it again, but this time, keeping your whole arm, from shoulder to finger tips as relaxed as possible, move your lower arm up and down from the elbow joint and allow your wrist to be moved through it's natural rotation by gravity only. Now try this again whilst holding a pick, do it slowly and watch the way the pick tip is angled up on the down stroke and as you raise your forearm gravity causes the wrist to rotate and the pick tip is now pointing down and ready to glide up across the strings.
Practise this movement until you are comfortable with it then transfer it to the guitar itself. Mute the strings with your fretting hand (sounds more pleasing to the ears that way) and start by slowly allowing the pick to glide down across the strings then reverse direction and glide the now downward pointing pick tip back up across the strings. When you can glide the pick smoothly across the strings in both directions, use a metronome and begin to up the tempo incrementally. Just remember that it is imperative that you remain relaxed and tension free - move the lower arm from the elbow joint and allow the wrist to rotate through it's natural arc.
Its worth mentioning that pick grip is a subjective subject, some like to hold it with a grip that keeps the thumb and lower fore finger parallel with each other - a grip that if find is great for picking and keeping a hold of the pick, but for me causes to much tension in the forearm for strumming. I personally prefer to hold the pick by pinching it between thumb and forefinger near to the tips. This does mean the pick is less secure but you will find that with experience you can manipulate the pick in your fingers as you are strumming without dropping it... and if you do drop it just carry on using your thumb and fingers!
So remain relaxed, move from the elbow and allow the wrist to act with gravity. It WILL become a natural and effortless movement eventually.
Edit: It also helps if you use a thin a pick as possible, this way you will have less resistance against the strings and less likelyhood of the pick shifting out of position in your grip.
