Guitar Tremolo Picking 101
Tremolo picking, sometimes called "up and down" picking, is someting that's a little difficult to start with only because many beginner players aren't instrcuted what not to do, which the above video covers. Things like what not to do for palm position, what not to do for strength of picking and how not to use your whole arm to pick when your wrist can do 99% of the work.
The only thing I didn't go into detail about are the picks used.
On electric guitars you can use whatever you want, but generally speaking it's easier if you purposely use a thinner pick such as Fender 351 picks in medium thickness.
On acoustic guitars it's a different story because you may not want so much "flap", as in pick noise. To decrease the flap, using a pick made of delrin with some good flex to it helps out a great deal, such as the Dunlop Tortex in .60mm size (the "orange one").
You'll have to experiment to see what works best for you depending on what type of guitar you're playing. With electric, the pick noise can be masked somewhat by the use of light overdrive/distortion. With acoustic there's nothing to hide behind, so to speak, so you'll have to use different picks to get rid of pick/flap noise.