Watch the Learn the Melody in Multiple Keys online guitar lesson by Fareed Haque from Solo Guitar Handbook
Learning the melody is the one step that most musicians don't do enough, and frankly, it's probably the most important step. Know the melody and then everything else can follow from there. Transposing is crucial as it shows you what is the same and what is essential about the melody and what is not. Learning the lyrics is essential in that it shows you how to phrase the melody and where the accents/important beats are. Once you really know the melody, the next steps all become easier. I Promise.
So go ahead and play the melody in C and E as in the examples, and try it in a few different octaves to really get the melody in your ears and fingers. Hey, and while you're at it, you'll be doing that weird thing called ear training. Obvious. Ears are like muscles. If you don't use 'em, they don't develop.
A little bit about "Amazing Grace" [from Wikipedia]:
"Amazing Grace" is a Christian hymn published in 1779, with words written by the English poet and Anglican clergyman John Newton (1725–1807). Jonathan Aitken, a Newton biographer, estimates that it is performed about 10 million times annually. It has had particular influence in folk music and has become an emblematic African American spiritual. Its universal message has been a significant factor in its crossover into secular music. "Amazing Grace" saw a resurgence in popularity in the U.S. during the 1960s and has been recorded thousands of times during and since the 20th century, occasionally appearing on popular music charts.
Here are the lyrics:
Amazing grace! (how sweet the sound)
That sav'd a wretch like me!
I once was lost, but now am found,
Was blind, but now I see.
'Twas grace that taught my heart to fear,
And grace my fears reliev'd;
How precious did that grace appear
The hour I first believ'd!
Thro' many dangers, toils, and snares,
I have already come;
'Tis grace hath brought me safe thus far,
And grace will lead me home.
The Lord has promis'd good to me,
His word my hope secures;
He will my shield and portion be
As long as life endures.
Yes, when this flesh and heart shall fail,
And mortal life shall cease;
I shall possess, within the veil,
A life of joy and peace.
The earth shall soon dissolve like snow,
The sun forbear to shine;
But God, who call'd me here below,
Will be forever mine.