How do I write an critical commentary on a passage I've never seen before?

Start by reading it multiple times, because the meaning of a passage or a poem can be tricky to grasp on a first reading, no matter how much you know about literature. The excerpt you're looking at will have an objective: the writing is trying to accomplish something, and that something will become more apparent the more familiar you become with the text.
Then, ask yourself some questions: what tone is the language constructed to convey? Is it bitter, lovelorn, anxious/tense, satirical (that's a big one - make sure you don't get the wrong end of the stick and misread a passage to be serious when it's not).
In general, passages will be divisible into two or three stages: that's how you should structure your essay. Describe the way the passage moves from one state into another, closely looking at the way that the language changes; do the sentences get shorter, creating tension; does the word choice of a poem shift to words which have connotations of a specific thing, like war, or pain? Always save time for a close examination of the ending, because there can often be a twist, or a climax, which needs discussing in your essay if you're going to get across the full meaning of your essay.
Finally, ensure along the way that you sprinkle in bits of context and alternative interpretations. "the author appears to be writing in the genre of tragedy (it is ok to hedge your bets just a little bit, if you are unsure about the genre of the passage, given that it is out of context), and this character, much like King Lear or Macbeth, appears to be sinking further and further into madness." "This might be read in x way, or perhaps we might also read it as y."