Watch the F Chord Pattern online guitar lesson by Stephen Mougin from Bluegrass Rhythm Evolution

For the F chord, pluck the D string (F note), strum, pluck the A string (C note), strum.

Once you get this under your pick, try an F chord that includes the low F note on the low E string, then pick the low E string and A string. While this has a fuller sound, the F is usually going to act as a 4 chord in C or a b7 in G so it doesn't need to be as "big" as the root chord in either key.