Literary analysis and argument construction are intimately connected. You might say they are two sides of the same coin.
In literary analysis, you take a literary work apart. You look closely at what is there and how it works. So, if you are analyzing a poem, you would look at the poetic structure. You would look at rhyme. You would look at rhythm. You'd look at imagery, metaphor, etc. You'd first look to see what is there: is there a formal structure? What is that structure? Does the poem rhyme? Which lines rhyme? You'd take notes methodically, moving through the poem a literary technique at a time. Then, once you had identified what was there, you'd move to a deeper level of analysis. You'd look at how these elements function. This might mean asking questions like this: "Okay, the first and third lines rhyme. What effect does that have on the reader?" You'd examine literary techniques individually, and you'll examine them together. So, you'd look at how rhyme and rhythm work together--and if they clash. The same with the images, metaphors, etc.
As you analyze, your understanding of that work should be growing. Eventually, it should be "ripe," and you can "pick" that understanding by constructing an argument about the poem. Your argument should use the results of your analysis as evidence.