To analyze a poem, you want to read it for overall content, identify major themes in the poem, and analyze it for literary devices the author used in order to illustrate the themes, messages, or emotions the author wants to convey. There are many different literary devices to consider and below is a link to a literary terms dictionary, but some common ones to consider are diction, imagery, and figurative language, such as similes and metaphors. If you need to analyze a group of poems, then it can also help to look for things the poems share in common, such as themes. Since access to some of the poems you have listed is limited, let's take a look at "Sheltered Garden" by H. D. and "Nativity Play" by Tilla Brading to help get you started. While the subject matter of both poems is completely different, both actually share the theme of the desire or need for liberty.
We can tell simply based on the title that the poem "Sheltered Garden" is about a garden. But more specifically, as we look at the refrain, "I have had enough," we know that the speaker is fed up with the garden. By the time we get to the third stanza, we see some very interesting imagery, such as "border-pinks, clove-pinks, wax-lillies, herbs, sweet-cress," which are all common flowers and plants one would see in a carefully landscaped garden. But why has the speaker "had enough" of seeing these flowers? The answer begins to be revealed in the fourth stanza:
[T]here is no scent of resin
in this place,
no taste of bark, of coarse weeds,
only border on border of scented pinks.
The images of the "scent of resin," "the taste of bark," and "coarse weeds" are all the sorts of things found in wild nature; hence, the poet's overall message is that the speaker is fed up with the garden because the garden is too carefully crafted; the garden is not like what's seen in the wild; it is not free. Hence, it becomes clear at this point that lack of freedom, freedom like in the wild, is one of the poet's major themes.
The same can be seen in "Nativity Play." This particular poem is about a completely different subject matter. It's all about what appears to be a child who is complaining about having to play a role in a nativity play. The child complains about wearing "some girl's neglige," which is a figurative way of describing the child's angel costume, and also complains about having to wear wings and a halo. The imagery used to describe the costume helps portray the child as being held captive by the costume; the child is not free, especially not free to do as he pleases. The two lines toward the end, "I don't believe in angels / they're something dreamed up...," are also very revealing with respect to the theme. Not only does the child feel he is being forced to wear the costume, he feels that religious beliefs are also being forced upon him; again, the child isn't free.
Hence, as you can see, just by analyzing two poems in terms of theme, imagery, and figurative language, we can see that both poems actually share the common theme concerning lack of freedom, which we can also call the need for liberty.