If you can play in the key of C, you already know how to play a normal F chord. F/C is played the same way. Just add in the C note on the 5th string, 3rd space, with your little finger. Similarly, the C/G chord is just a normal C, with the G note added in on the 6th string, 3rd space, again with the little finger.
If this is too much of a stretch for you, substitute a normal C, and start working on some finger stretching exercises. My favorite is to spread the little finger and ring finger of the left hand by placing two fingers of the right hand between them for ten seconds. Then place three fingers between them for ten seconds. Then do the same between the middle and ring fingers. Then do the same between the index and middle fingers. You can do these exercises unobtrusively anywhere. Done several times a day, this should loosen up your fretting hand fast.
A couple of tricks to make this piece even easier:
-- When playing a C chord, and the tab calls for you to fret the 3rd string, 2nd space (A), it’s usually easiest to do so by flattening the middle finger across the strings briefly, rather than moving the whole hand.
-- When doing a pull-off on the 3rd string, as in the second measure, starting and ending with a C chord, it may be easier to do it as a push-off instead. It will sound the same, but you don’t need to release and re-fret the chord, which slows you down a lot. Trying to do the pull-off without releasing the chord is awkward, and makes for a weak pull-off.
William Clayson (1840–1887) was a Latter-day Saint hymn writer who wrote the music of "The Day Dawn is Breaking"; "Nearer, Dear Savior, to Thee"; "Hope of Israel"; "O Thou Rock of Our Salvation"; "The Iron Rod" and "Oh, What Songs of the Heart".
Clayson was born in England. He joined The Church of Jesus Christ of Latter-day Saints (LDS Church) in 1855. In 1859 he served as branch president in Irchester. In 1861 he emigrated to Utah Territory, settling in Payson, Utah. He married Susan Moulton in Utah who he had become engaged to before leaving England. He was associated with the LDS Sunday School in Payson, and all his hymn tunes were written as accompaniments to words by Joseph L. Townsend, who was also associated with the Sunday School in Payson.
That’s all I know about the composition and lyrics of this song. Does anyone know any more?