So you've found the "about the manga" section! I can't remember exactly why I wanted this in my Vash shrine, but since I made a link for it on my layout, I suppose it couldn't hurt anything... except my reputation as a "character shrine" as opposed to a "general info page" :p
Trigun started out as a manga series running in the Shounen Captain Comics manga anthology, written and illustrated by Yasuhiro Nightow. If I'm not mistaken, this anthology folded and Trigun was paused after three volumes, and it is these three volumes on which the anime is based, and the anime stayed pretty faithful to most of the early manga stories. Trigun ran in Shounen Captain Comics from 1995-1997.
For the unitiated, a manga anthology is how comics are initially distributed in Japan before they are collected into volumes. Every manga title runs in some anthology or other, and there are literally countless anthologies published in Japan. The frequency of these varies, from weekly to monthly, biweekly, bimonthly, quarterly, annualy, etc. They are generally several hundred pages long and very thick, and are therefore nicknamed "Phonebooks." Though they are thick, they are generally very inexpensive and are printed on extremely cheap, usually multicolored newsprint and are meant to be thrown away after your perusal. Popular shounen anthologies include Weekly Shounen, Shounen Sunday, Shounen Ace, GanGan, and, of course, Shounen Jump.
After Shounen Captain Comics folded, Nightow switched publishers and Trigun moved to Young King Ours, a monthly anthology that publishes such titles as Excel Saga, Hellsing, and Geobreeders. Generally, when a manga series switches publishers, the name will change, and Trigun was no exception. It runs to this day in Young King Ours as "Trigun Maximum." The Trigun Maximum manga story is actually much, much different and more surreal than the anime, you'd be surprised ^_^ The events, characters... nearly everything is completely different in Trigun Maximum than the anime. But don't get me wrong, Trigun Maximum is the CONTINUATION of the Trigun MANGA SERIES. There's no difference except the title. It's much different than the ANIME, but is the official manga release of the series. If Trigun hadn't switched publishers, there would be no name difference. Right? Right. So Trigun Maximum is the continuation of the Trigun manga. There is no difference in story between the two. Just so that's clear, because a lot of people are confused about it. There are currently 9 volumes published, and it supposedly is ending soon... which might be a good thing considering all the stuff Vash and Wolfwood are going through in this series ;_;
The original 3-volume Trigun series that ran in Shounen Captain Comics was reprinted in a Young King Ours edition. The YKO version of the original Trigun is two extra-thick volumes with new cover art by Nightow. This two-volume YKO edition is what the English version is based off of.
As an extra side note, aside from doujinshi (fan comics), Trigun is Nightow's first manga series. So lucky to have such a hit on the first try!
If you're looking to buy the Trigun manga, I'd highly recommend Sasuga Books, they have all the books instock (including both editions of the original "Trigun" series) and generally do a good job getting ahold of stuff for you, I've ordered some obscure CLAMP stuff from them before. The English edition (which is WONDERFUL and you should have no second thoughts about buying) should be fairly easy to find, Dark Horse is generally carried in most bookstores, and Trigun's fairly popular, so you should have no trouble finding it. If you'd like to order online, you of course can't go wrong with amazon.com.
For differences between the anime and manga incarnations of Vash the Stampede, please see the "differences" section ^_^