A good place to look for a critical analysis of any literature or poem is in literary journals and scholarly websites. Enotes also has great commentary on many of Percy Bysshe Shelley's poems, and that might give you some background information that will be helpful. I provided links below to those sources.
"The Moon," is a long, dedicatory poem written to the moon, in adoration and awe of her. Shelley had a penchant for writing poetry to different forces of nature; his more well-known counterparts to "The Moon" are his poems on the west wind ("Ode to the West Wind"), clouds ("The Cloud"), and skylarks ("To the Skylark"). "The Moon" is another one of these poems; in it, he contemplates the moon, its significance, its beauty, its symbolism, and its impact on people looking up at it. The most heavily used poetic technique that Shelley applies is that of personification, where he gives the moon human-like traits, to make it seem like it is a human being, and not an inanimate object. This endows the moon with a definite personality, and layers of depth that enhance its beauty and profundity. For example, consider this stanza:
"AND, like a dying lady lean and pale,
Who totters forth, wrapp'd in a gauzy veil,
Out of her chamber, led by the insane
And feeble wanderings of her fading brain,
The mood arose up in the murky east,
A white and shapeless mass."
In this stanza, Shelley compares the moon to a woman who is dying, losing her mind, and stumbling about in the dark. This makes the moon seem infinitely sad and pitiful, and gives it a complexity that just describing its beauty would have left out. He personifies it in many different ways other than a dying woman, and each new way adds depth.
Shelley also uses imagery, or the five senses, to describe the beauty of the moon. He also applies rhyming techniques to give it a flow and rhythm. There isn't enough room to discuss all of the poem or its techniques, but I hope this helps you to at least get started. Good luck!
In the first stanza the poet descibes the moon with an old lady who is sickley and dying.And in the second stanza he compares the moon with a young lady. And he says that " of climbing heaven and gazing on earth" as if the moon has died and has reached the heaven...and is watching the earth from all above.
In the 1st stanza as the poet describes the moon as a dying lady he says that she is lyk a dying lady who is sick and pale. pale because probably she has no blood in her body because she is in her death phase and lean because she is old. This poem can also be told to be an alligory because its each line has two meanings. He rather describes the moon to be senile because it was during the dusk time when the moon was rising and thus it looked pale. He has also told that the moon is wrapped in a "gauzy veil" i.e by some thin or transparent cloth. and here the 'gauzy veil' has been compared wid clouds. This is because when da moon was rising it was dusk time and the faint beam of sunlight was still their which made the tym look gloomy and the clouds wrapped up the moon lyk the veil. The sky was yet to be dark so the moon wase'nt bright enough so the poet compared the old lady's (the moon's) brain as a fading one as she was feeble and she was wandering. This is to be noted here that in the two stanzas the poet has described the moon to be wandering. But thr is a big difference in both the cases. In the first stanza the moon wonders because she is old,feeble,sickly and she totters as she dosent knw whr to go. Bt in the second stanza she wanders because she is alone and she is in search of a companion. He also says that the moon arose in the murky east this is because the sun was setting and the tym was gloomy. The moon seemed to be a shapeless mass because it it was still not a full moon yet.
In the second stanza he says "art thou" dat is he directly addresses the moon. These words make it clear that the poet is offering an idealsed description of the moon in the traditoin of medieval love poetry. And he says that the moon is "pale for weariness" dat is because the moon is tiered of serching a companion for herself. And then the moon climbes the heaven and watches the earth.This means that the moon is now high up in the sky, because the sun has fully set by now and the dark hours have started. He says the moon is lonley among the stars because they have a different birth and so she remains lonely and keeps on changing lyk a joyless eye. Her eyes are joyless because she has no companion and she changes because a moon has its different phase. And we see the moon sometimes partly sometimes full and so on. And in the last line the poet say " that finds no object worth its constancy" i.e the moon realises that no one truly deserves her love and so she remains alone comapionless for ever in her own heavenly world wrapped with sorrow.