Rhyme schemes basically identify sounds at the end of lines in poetry, with a letter assigned for each new sound.
Shakespearean (also known as Elizabethan) sonnets have the rhyme scheme of ABAB CDCD EFEF GG.
Italian (also known as Petrarchan) sonnets have the rhyme scheme of ABBA ABBA CDE CDE (though there are other forms of this kind of sonnet).
The Spenserian sonnet's rhyme scheme is ABAB BCBC CDCD EE.
To understand the rhyme scheme, it helps to remember that each letter represents a sound, and the same letter repeated indicates words that rhyme—based on the LAST word of each line.
In "The Vanity of Human Wishes" by Samuel Johnson, the first "stanza" has twenty lines. (The stanzas are long.) In charting a rhyme scheme, a new letter is used for each new sound. The lines are paired and rhyme in this poem: these pairs are called rhyming couplets (as in "couple").
In charting rhyme schemes in the past, my understanding is that with each new sound, a new letter is assigned for that new sound. With this in mind, the first two lines that end in "view" and "Peru" are assigned the letter A. The next pair of lines rhyme with each other, but not with the first two lines, so the letter changes for the new end rhyme in those lines. The next two, "strife" and "life" are assigned B, and so on.
Based on my understanding of charting rhyme schemes, the rhyme scheme for this poem is:
AA BB CC DD EE FF GG HH II JJ.