Rhyme scheme is defined by looking at the last word of each line of poetry. In regards to the poem in question, "The Oak" by Alfred, Lord Tennyson, the last word of each line of poetry is as follows (spaces between words denote stanza breaks):
Life, old, oak, spring, gold.
Rich, then, changed, hued, again.
Leaves, length, stands, bough, strength.
To begin to determine the rhyme scheme, take the last word of the first line: life. Life is denoted with an "a."
The next word is old. Old does not rhyme with life, so it is denoted with a "b." Following old is oak. Oak does not rhyme with either life or old, therefore, it is denoted with a "c." The next word under consideration is spring. Spring does not rhyme with any of the previous words and is denoted with a "d." The last word, in the last line of the stanza, is gold. Gold rhymes with old and it is denoted in the same way as old is; with a "b."
When looking at different stanzas, you must still take into consideration the previous words and rhymes. Therefore, when examining rich, it does not rhyme with any of the previous words and the lettering continues. Rich is denoted with an "e."
To finish the rhyme scheme, simply examine each of the remaining words and see if they rhyme with any of the previous words. If they do not, they take on the letter following the last one used. Any words which rhyme with a previous word takes the letter of the rhyming word.
Therefore, the rhyme scheme of the poem is as follows:
a,b,c,d,b e,f,g,h,f i,j,k,l,j (if divided into stanzas)
a,b,c,d,b,e,f,g,h,f,i,j,k,l,j (if no spacing is used to denote stanzas)
ABCDBEFGHFIJKLJ (if teacher prefers capitol letters and no commas)
A,B,C,D,B,E,F,G,H,F,I,J,K,L,J (if teacher prefers capitol letters with commas)
Be sure to know how your teacher wishes you to denote rhyme scheme. Some teachers prefer, and teach, the denotation of rhyme scheme in a very specific way.