Watch the F Chord online guitar lesson by Marcy Marxer from Swingin' Rhythm Handbook
The F chord position shown here is a full handed clutch position. If using your thumb doesn't work for you, a barre chord will work just fine. There are several ways to play a moveable version of an F chord in the first fret.
Playing the first 4 strings or strings 1, 2, 3 and 4 gives you a moveable F chord on the high strings. Playing strings 2, 3, 4 and 5 gives you a lower inversion and a deeper sound and uses C as the bass note.
Playing strings 3, 4, 5 and 6 gives you the lowest inversion and a clear F bass note. That F bass can be fingered by making a barre with your 1st finger or by reaching all the way around the neck with your thumb.