It's a good idea to compare the details and themes of the two versions, both for similarities and differences. Get started by noting that the second story lacks the grand structuring principles of the first. There's none of this first-day-second-day-let-there-be stuff.
FYI, the deity's name is slightly different here than in the first account of creation. Instead of the name God ('elohim in Hebrew) you will find the name Lord God (YHWH 'elohim in Hebrew).
Using the name Lord God is a very personal way of referring to the deity. It's kind of like his private nickname.
This account starts with the earth and heavens already in place. There are just no shrubs or plants yet.
There's no rain or humans to do all the work yet either.
With no rain, the water's got to boil up from below to saturate the soil. Weird.
The deity forms a "man from the dust of the ground" (2:7). If you look closely, there's a cool pun in the Hebrew. The word for "man" is 'adam and the word for "ground" is 'adamah. Aha.
The deity breathes life into the man's nostrils. Don't try that at home.
Then he plants a garden in Eden and puts the man there.
Every luscious and beautiful tree grows in the garden at God's command, including "the tree of life" and "the tree of the knowledge of good and evil" (2:9).
Eden is watered by a river, and the river divides into branches named (1) Pishon, which goes through Havilah (where there's gold), (2) Gihon, which winds its way through Cush, (3) Tigris, which runs to the east of Ashur, and (4) Euphrates.
The man is supposed to take care of the garden.
God lays down some ground rules for the man. He's not allowed to eat from the tree of the knowledge of good and evil. If he does, he'll have to become a being who dies. (You probably know how this one ends).
God decides to find a suitable partner for this poor lonely guy. He'll need a "help meet" (2:18 KJV), whatever that is, or (even better) a "helper" (NRSV). Robert Altar translates the difficult Hebrew a "sustainer beside him." Take your pick.
God creates a bunch of animals of all kinds.
The man gets to name all the creatures, "dog, turkey, cow," but none of the creatures are suitable mates. We sure are glad about that.
Next up, the deity puts the man under with a heavy dosage of divine anesthetic and removes a rib from his side to create the woman.
God presents the handiwork to the man, and he's glad to see her. He names her woman (Hebrew: 'ishah) because she was taken from man (Hebrew: 'ish).
And that's why people get married—to become "one flesh."
The husband and wife are buck naked, even after their honeymoon, and they don't have a problem with that. Nice.
So, yes, this is very different from the first creation account. There was definitely nothing about nudity in the first story.