How would you go about analysing an unseen poem for the first time?

I think the clearest access point when starting to unpick a new text is through identifying key themes, motifs and patterns, which can be pretty easy once you know what you're looking for. There are a couple of techniques I've noticed over time that work relatively well. As an example text, I'll use Shelley's Ozymandias. First thing to look for, almost always, is structure and form; does it rhyme? Does each line meet a specific syllable count? In this poem, you'll notice moments with rhyming couplets (two rhymes) and tercets (three rhymes); "antique land", "on the sand" and "cold command", one lines 1, 3 and 5, for example, or the last four lines, which use alternating rhyme (where the first and third line rhyme, as do the second and fourth). Once you've noticed anything structurally interesting like this, it is helpful to underline or highlight it in one colour. Then, with other colours, start to identify themes, by noting down words which draw on similar ideas and images. I would, for example, underline "antique", "lifeless", "decay" and "bare" in a different colour as markers of the theme of 'Age', and also "ye Mighty", "colossal", "pedestal" and "Kings of Kings" in another colour as markers of 'Nobility and Power'. Once you've got the poem annotated like this, you have a clear entry-point to start analysing the poem and the way it communicates ideas and motifs.