I walk up the muggy street beginning to sun and have a hamburger and a malted and buy an ugly NEW WORLD WRITING to see what the poets in Ghana are doing these days
New stanza. The speaker has been thinking about the rest of the day, but now he returns to the present moment. Presumably, after the shoeshine.
He walks up the street, eats a hamburger and a "malted" milk shake, and buys a literary journal called "NEW WORLD WRITING." We're not sure why he puts the title in caps.
It's July, remember, so no surprise that the street would be "muggy." The speaker is even "beginning to sun" – he's got a little tan going.
New World Writing was a literary magazine published during the 1950s. It was an "anthology," meaning it contained samples of work by many different writers. Many of the "big names" in Western literature published their work in it, including Joseph Heller, Jack Keruoac, and Samuel Beckett.
Notice, though, how our speaker seems distinctly unimpressed by the magazine. He makes fun of its "ugly" color and cracks a joke about seeing "what the poets in Ghana are doing these days." In addition to big-name Americans and Europeans, New World Writing published authors from around the world, and the 1950s were the time when African writers became popular in progressive intellectual circles.
You could interpret the speaker's attitude as skeptical ("Why is everybody suddenly so interested in these poets from Ghana when nobody cared before?") or as merely curious ("Ghana, huh? Small world").
Either way, he's not amazed. This is a guy who has seen literary fads come and go.