[Alfred]

For fat fingers the best answer (but not the quickest or most comfortable to learn) is to follow that link Michelle gave you and learn barre chords. Barre chords will open up a whole new world for you.

Some other choices are to play the Fmaj chord and leave the e string open. It will sound different but should fit most situations. You could also move the d shape chord up 3 frets and just play the top 3 strings (g b e string)