Analyzing a poem is not a "paint-by-numbers" scenario, but you can always start by considering the same key aspects when writing an analysis. For this poem, the most obvious place to start is probably with its style and structure.
This poem is often referred to as a prose poem; more specifically, it is written in free verse. It can be difficult to determine where poetry ends and prose begins, but the layout of the words on the page indicates that this is to be understood as a poem, despite the fact that it has no rhyme scheme, regularity of line length, or continuous meter as is the case in blank verse (which tends to adhere to iambic pentameter). The great benefit of using blank verse for a poem such as this, which offers advice as to how life should be lived, is that it allows the poem to be read as if we were in conversation with the poem. Freed from the conventional stylistic trappings of poetry, the poem becomes more naturalistic, which creates an intimacy between poet and reader and allows the words to penetrate more deeply.
The tone and language of the poem also support this intention. In mood and attitude, the poem is gently advisory; it urges the reader, addressed directly in the second person as "you," to "be cheerful" in what is "still a beautiful world" despite its many shortcomings.
One of the techniques the poet uses repeatedly is the direct command: "Be cheerful," "Be yourself." The parallelism in these brief sentences contributes to the emphasis that is placed upon them: in their brevity, they stand out from the rest of the poem as its most salient elements. Throughout the poem, the poet varies between the use of long sentences with enjambment (where a sentence continues without interruption over the end of a line and into the next) and the use of these shorter, commanding sentences, which are almost used as punctuation.
The figurative language in this poem is sparse, which means that it is more important when it does appear. For example, the poet describes love as "perennial as the grass," a simile which creates an interesting visual image. Like grass, the plant which is universal and can never be killed, we imagine love as enduring through the many ages of the earth. Likewise, "strength of spirit" is imagined as a "shield" against sudden misfortune, emphasizing the value of that strength.
The ultimate conclusion the poet reaches in his address to the unnamed reader is that "whatever you conceive [God] to be," we should strive to be "at peace" with him and with ourselves. The note upon which the poem ends--"strive to be happy"--is an uplifting one, leaving the reader feeling encouraged and motivated.