"Civil War: Peter Parker, Spider-Man" actually collects issues #28-34 of "The Sensational Spider-Man" (Marvel's "Peter Parker: Spider-Man" title ended in 2005 when it was relaunched as "The Spectacular Spider-Man," while "Marvel Knights: Spider-Man" was renamed "The Sensational Spider-Man" in 2006--it only sounds confusing). However, as the title for this collection of stories indicates, the emphasis here is on the impact on the life of Peter Parker now that the world knows he is Spider-Man. You should already know that Marvel's Civil War event has to do with the passage of the Superhuman Registration Act, which says every superhero who does not reveal his identity to and register with the government is going to be treated like a super-villain. When Iron Man reveals that he is Tony Stark, Peter decides to follow suit and reveal his secret identity as well.
The first story in this collection, "My Science Teacher is Spider-Man," is about what happens when both Peter's students at the high school and Dr. Octopus learn that particular fact. That is followed by a three-part story entitled, "The Deadly Foes of Peter Parker." Tony Stark had told Peter that things will change once he comes out, but insisted "it's not like every deviant personality you've ever crossed swords with in the past is going to start coming after you now." But the Chameleon, Molten Man, Scarecrow, the Green Goblin, and Will-O'-the-Wisp all show up in the first ten pages to suggest otherwise (and wait until you see who is behind this organized assault on the Web-Head). Meanwhile, if Peter is now a public target the same holds true for Mary Jane, who has to fend for herself since her husband is being attacked on the other side of town. However, that leaves Aunt May on her own as well, when one of the bad guys goes after her (poor super villain does not stand a chance).
Both Peter Parker and Spider-Man are minor characters in the remaining three stories, as the women in our hero's life deal with the brave new world in which they now find themselves. "The Husband or the Spider?" focuses on Mary Jane, who remembers a dream from long ago when she decided to marry Peter and who has a very interesting talk with Sue Richards, the Invisible Woman, whose marriage to Mr. Fantastic is also having problems because of the Civil War. Old "Wounds" are opened for Aunt May when she takes care of Peter while he heals from his latest beating, remembering what it was like when he was a boy and she was raising him. Finally, Felicia Hardy (a.k.a. the Black Cat) shows up to help in "Nothing Can Stop the Rhino." Of course, trying to stop the Rhino is exactly what she is going to do, spurred by the long and tangled relationship she has had with Peter. The ending of this one is certainly unusual, but reinforces the idea that this is a series of character studies and not just another round of comic book battles.
Overall the stories in "Civil War: Peter Parker, Spider-Man" constitute a series of backstories to the main action during this period that is covered in both "Civil War" and "Civil War: Amazing Spider-Man." By the time we get to those last three stories in this collection Peter has changed his mind about the SRA and is now being sought by Iron Man and the government. That explains why he starts out in the latest new costume, the red and gold one designed by Tony Stark, and then ends up back in the familiar red and blue costume (in issue #35 Spidey is "Back in Black," ostensibly because he is outside the law once again, but really because the black costume/symbiot plays a big role in this summer's blockbuster "Spider-Man 3" movie). Roberto Aguirre-Sacasa is the writer for all of these stories, with Clayton Crain doing the art for the first one, and penciler Angel Medina and inker Scott Hanna doing the next four, Hanna inking Sean Chen's pencils for the final pair of stories. Collectively, these seven stories represent an attempt to try to stop and take stock of Peter, Mary Jane, and Aunt May now that everything changes--and changes again--because of the Civil War.