Find the comic book in the "Back Issues" section of a local comic shop. If you don't know where a local comic shop is, use the Comic Shop Locator website to find one. As of April 2011 the title in "near mint" condition is valued at $12, which means you shouldn't have a hard time finding it in the "Back Issue" bins at the shop.
Purchase the "Spider-man: Carnage" trade paperback. In comic book terminology, a trade paperback is a paperback collection of multiple issues in an original run of comics. The "Spider-man: Carnage" trade paperback collects all issues that represent the origin of the character Carnage, of which "Amazing Spider-man" #344 is a part.
Purchase the "Spider-man: Venom Returns" trade paperback. "Venom Returns" was released close to the time of the third Spider-man film and collects notable issues in the history of the character Venom. The character of Carnage is closely tied in with the origin of Venom and "Amazing Spider-man" #344 is found within this collection.