Comic books usually start at #1 and increase from there.
For example, the seminal, Earth-changing comic book Watchmen was originally released as 12 comic book issues: Watchmen #1 through to Watchmen #12, the final issue.
For another example, popular comic book Superman/Batman started with Superman/Batman #1 in October 2003* and has been increasing steadily since then, with no signs of coming to an end anytime soon.
However, it is rarely a good idea for a collector to put his comic books in strict numerical order, because the comic book companies will often screw about with the numbers. Here are some potential trip-ups you can expect to find:
By far the most common numbering quirk you'll find. Issue #0 of a given comic is typically given over to exploring the origins of the character or characters you'll find in that comic. The problem? While Issue #0 is often issued immediately before #1, equally often it is released some time later down the line. Stormwatch #0, for example, was released in August 1993, between Stormwatch #3 (July) and Stormwatch #4 (October).
A more complicated example is the most recent Supergirl title, which started with #1 in October 2005 - but what you may see described as "Supergirl #0" is actually Superman/Batman #19, which was released in May of that year, following on from the Supergirl character's introduction in an earlier Superman/Batman arc.
Ultimate Vision #0, meanwhile, was actually originally released in several parts. There was a month in which each Ultimate Marvel comic book had a backup story, made up of several pages from this single Ultimate Vision issue. The idea was to build anticipation for a forthcoming event. It wasn't until much later that Ultimate Vision #0 was released as a single issue.
As a more memorable example, the September 1994 conclusion of DC's line-wide crossover event Zero Hour saw a villain remake the DC Universe's timeline from start to finish with subtle timeline alterations. As a result, each extant DC comic at the time - of which there were forty - ran an issue #0 in October 1994 which recapped the recently-tweaked origins stories of the heroes.
Zero Hour is worth further study. As a five-issue miniseries featuring the corruption of the DC Universe timeline as the central plot point, the series began with Zero Hour #4 and ran through #3, #2 and #1 to the final issue, Zero Hour #0.
The Invisibles volume 3 also counted backwards, from #12 to #1.
Countdown, a weekly comic started in May 2007, did the same thing, going from the first issue (#51) to the last (#1) over the course of a year.
I only know of one or two issues that are actually numbered #½. These seem to be special promotional issues when they do crop up, and aren't the full length of a regular issue. There is also Elfquest: Hidden Years #9.5 and some others.
In November 1998 DC ran another line-wide crossover which involved time-travelling to the year 85,271 - precisely one million months after Action Comics #1 was released in June 1938, and therefore the likely year in which Action Comics #1,000,000 would be expected to come out if nothing happened in the meantime.
Anyway, all DC's comics ran a one-millionth issue to coincide with the event - roughly half of these directly linked in with the events of the crossover, while the remainder explored what the featured heroes or their descendants would be up to in the 853rd century. So, for example, Detective Comics #726 is followed by the DC One Million crossover (which includes Detective Comics #1,000,000) and then by Detective Comics #727.
Not using regular numbers
I've only seen this once: The first series of Gen¹³ has #12 followed by #13A, #13B and #13C (each shorter comics than usual) then #14.
In April 1994 the then-fledgling publisher Image ran a promotion called "Images of Tomorrow". Each extant comic book title, whatever issue number they were currently at, jumped forward to issue #25 - as many as two years into the future. The idea was to give a tantalising glimpse of what was going to happen in the not-to-distant future of Image comics, and for the titles to work their way towards these events afterwards - so that when issue #24 arrived in the normal passage of time, #25 slotted in neatly and #26 followed on directly afterwards. As a result... dang it, I need to read more comics, I'm back to Stormwatch again. Stormwatch #9 was followed by Stormwatch #25 which was followed by Stormwatch #10.
From a more corporate point of view the aim was to show that Image was going to be around for a while. At least for a few more years. There was scepticism at the time but I believe that in fact it worked out quite well. Certainly Stormwatch made it to issue 50 and kept going after that. Which brings up another fun one:
Randomly restarted numbering
Amazing Spider-Man began in March 1963 and ran from Amazing Spider-Man #1 to Amazing Spider-Man #441 in November 1998, at which point the run - known as "Amazing Spider-Man volume 1" or "Amazing Spider-Man (first series)" to fans - terminated.
But ASM returned in January 1999, restarting from Amazing Spider-Man #1.
Restarting comic book numbers is perfectly standard practice. There have been three series of comics titled "Wonder Woman", four titled "Green Lantern", and is it five for Hawkman? After all, a three-digit issue number is intimidating for new readers; also, some characters just vary wildly in popularity, or eke out a living in miniseries after miniseries. (Admittedly DC have more of a problem with this than Marvel, who prefer to add adjectives to differentiate their many comics.) In this case in particular, there had been a clean break between the two series, so who cares?
I'll tell you why this particular example gets confusing:
Randomly resurrected numbering
Amazing Spider-Man v2 #58 came out in December 2003. It was followed immediately by a comic book entitled "Amazing Spider-Man #500".
That's right. They went back to the old numbers, retroactively reclassifying ASMv2 as a continuation of ASMv1. It's fun, fun, fun following comics!
This isn't really a numbering thing but it's worth mentioning. Comics change their names sometimes. For example, the most recent Hawkman title became Hawkgirl not long back, but the numbers just kept going: Hawkman #49 preceded Hawkgirl #50.
Likewise, some years ago the original Superman title - you know, the one that started in 1939 - changed its name. Superman #423 which came out in September 1986 was followed by Adventures of Superman #424 in January 1987. Adventures of Superman continued for nearly two more decades, until the title was changed back, with AOS #649 being followed by Superman #650.
And if you think that's bad? At the same instant that Superman v1 renamed itself to AOS, a new Superman comic book was begun with Superman v2 #1. And, at the same instant that AOS renamed itself back to Superman v1, Superman v2 ended with issue #226.
Since the volume numbers don't appear in the comics' titles, this means a naive attempt to follow the "Superman" comic book would result in you reading Superman #421, #422, #423, #1, #2, #3, ..., #225, #226, #650, #651, ...and so on. Insane!
Often you will find a crossover story which oscillates between two, three, or even seven different comics at once. For situations like this I find it easier to call the whole crossover story a separate "title", and put all the comics within the crossover in reading order, but keep them in a separate block.
One-offs, and those with no number at all
Lastly, watch out for annuals and things. Generally these get called things like "Giant-Size Hulk #1" but may still fit firmly in continuity between consecutive comics. (Or they may not.)
Other screwy stuff they haven't tried yet and hopefully won't
One thing I did want to try was a comic called Power of Two, where every year a superhero appears on Earth, each twice as powerful as the previous one. You'd start with an ordinary human being in issue #1 and build up the powers and issue numbers as you go #2, #4, #8, #16, the world getting more unstable all the time... Yeah, it might suck, but who cares? A man can dream.
* All dates in this article are cover dates, which are generally about two months after the date they are actually released so they don't look old on the shelves.