How are people able to figure out the poems' meanings?
If you are distressed by not comprehending poetry which uses much of metaphor and other devices you might truly enjoy the poetry of Philip Larkin who, while not using one poetic style throughout, has many many very literal poems..so even so, you can then benefit, enjoying his often amusing, profound and emotional plain language. I hope so, as you want to understand and he might lead you further in your confidence to find similar poets. John Masefield too, is a maestro of atmosphere without being obscure.
Education and Experience. Nobody is born knowing about poetry, you need to learn about the language, the multiplicity of meanings, the way sounds work and the nuances the selection of a particular word can bring to a piece. A song like American Pie is just a nice ditty until you know the 'Day that Music Died 'refers to the death of Buddy Holly and Ritchie Valens in a plane crash. It is possible to over-analyze - just read them for the images they evoke. Something like The Lady of Shalott has heaps of literary techniques and tricks, but like a huge tapestry you can enjoy the tale of the doomed imprisoned lady. You might infer that the sense of detachment (as if reflected in a mirror) suggests Tennyson's own view of the society he inhabits, but that is one interpretation. Good poetry should be more than the sum of its words. Look at as many poems as you can - Stevie Smith, Dylan Thomas, John Drinkwater and consider what they are writing about and why.
All humans base reactions on THEIR Perceptions & emotional state of being. IE: Each individual will see or hear through there OWN "Filters"
Most people miss what the theme of a poem is, because it's usually simple and subtle. Without the theme, you'll miss the meaning. So the first thing to do is figure the theme out, and then figure out the meaning.
There's a famous quote from a poem by Archibald Macleish "A poem should not mean but be." When I was teaching at university, my office was next door to two English profs. They would have students come to them for help and sometimes it involved the meaning of a poem. I'm sure they thought me a philistine because my field was chemistry. However, I love poetry; I have since I was a child. Anyway, I wanted to scream at them because they'd tear a poem apart and analyze every word sometimes. I thought it was both arrogant and insane. I still feel it's arrogant to assume that your meaning of a poem is the only valid one and that it's insane to tear a poem apart as if destroying the sound, rhythm, and often, the context is justifiable. In an attempt to chastise them I placed a line on my door in German written by Rilke. I'm sure they couldn't read it, but it said in English, "You kill all things for me with words!" Don't concern yourself with wondering if your interpretation of a poem is "right" or not. Read a poem for the sound and the enjoyment of whatever meaning you take away. If you don't take away anything, that's okay too. All poems don't speak to everyone. Take pleasure and delight in those that do.
People who are very literal, such as people with Autism or other cognitive problems, can't understand poetry because they don't get similes and metaphors. If you don't get how a brook can 'babble' like a human voice, you may not be able to understand metaphors at all. But poetry is also about narrative, i.e. telling a story. This is done in many popular songs, very often about how she broke his heart, or vice versa. Anyone who can understand conversational English ought to be able to understand this kind of poetry.
Intelligence and experience.