Playing fast songs will require you to be able to switch between chords quickly and hold onto the pick to play rhythmic strumming patterns. For starters, play all eighth notes with a down strum. For any fast song, this is a good starting point. You DO NOT have to play all the strings on every beat when you are playing a fast song. On the D chord, just play the bottom 3 or 4 strings. On the 1 beat of every measure, try to play the full chord and include the bass note. On the other beats, as the bass note rings out, you will play the higher 3 or 4 strings. Your main goal is to NOT BREAK THE RHYTHM. If you have to start slow, that is OK. Most of you will have to start slow!
A popular pattern for many fast songs is: G C D C
This is the chord progression for the popular song “Every Move I Make” as well as many others.