¯\(º_o)/¯ is a meme that originated from the original Japanese Yotsuba bulletin board. It is often accompanied by the words "i dunno."
The first appearence in 4chan was a post, "i'm a faggot, lol! ¯\(º_o)/¯", by Anonymous. While influenced by Japanese Shift_JIS emoticons, the special characters exist in the ISO 8859-1 encoding. Codepoint AF is the macron (hands) and the left eye can be either Codepoint B0 (degree sign) or BA (ordinal character). The Unicode codepoints are U+0304 and U+00B0/U+00BA respectively.
How do I shot web?Something Awful) were playing NS when a lot of newbies and clueless people were on the server. "how do i shot web" was one of the questions that kept coming up. Someone took a screenshot, posted it to FYAD, and it went from there.
Most commonly seen on /b/ as an image macro, featuring Spider-Man holding out his arms in an "I dunno..." gesture; this later inspired a series of shopped images, including one with a Japanese newscaster holding out his arms in the same gesture (along with Spider-Man and a number of anime characters), and a meme where a picture of a falling person is shopped to say "Hey Spider-Man, how do I shot web?" (with Spider-Man replying "dunno, lol"). Juliet Nao Zhang from the anime My Otome, who has spider-themed powers and a robe which bears a passing resemblance to Spidey's costume, has also been spotted in shopped screenshots asking the question. When Mitchell became An Hero, his faced was also shopped over spiderman's, with the text "How do I shot self?"