By now you should have a decent idea of what to expect (and not to expect) in Japan and what you'll need to do to get ready if you want to be an ALT (Assistant Language Teacher) there. At least assuming that you read the first two parts of this guide. If you haven't, I highly recommend you check them out before continuing on. After all, moving to another country to work, even if it's only for a year or two, is a huge step and you really shouldn't jump into it without proper planning.
But enough of the warnings. You want to be an ALT, right? So, let's cover the basics of actually finding a job.

Types of Jobs:
First off, there's two main types of ALT jobs in Japan and they're a lot more different than you may think. Here's a quick summary of both. Take a look and think about which you'd prefer. Though, keep in mind that if you really want to be an ALT you might just have to take whatever position you can get, even if it's not the one you wanted. In both types of jobs the average salary is about the same and both will usually help you get a visa, find an apartment, and all that. Also, many ALT companies have a sample contract somewhere on there web site Find it and take a close look at the details, there's usually some things they don't mention or gloss over on the main site.

Public Schools: If you're hired to work in public schools you'll most likely be working with elementary and/or junior high students, though preschool and high school are possible as well. Depending on the school district, you might end up spending all your time at one school or going back and forth between a few of them. You'll be on a public school schedule so you'll most likely have weekends and Japanese holidays off along with a handful of personal days (though some public schools like their ALTs to came in on some Saturdays as well). Working hours will likely be something like 8-5, though you may be asked to "voluntarily" stay late to help students with English related projects. You probably won't get a true break, but you might end up with quite a lot of down time during the day. You may or may not have a curriculum to follow as well. You'll be working with Japanese teachers (either English teachers or homeroom teachers) and your working experience and the amount and type of work you'll be doing will vary considerably depending on said teacher(s). Get some good ones and you'll have a great experience, get some bad ones and you could be in for a really rough time.

Private Language Schools: Technically, at private schools you're usually an ELT instead of an ALT but anyway... In private language schools you may have to work with people of all ages, from kids to seniors. You'll most likely be working at only one school but you never know. Your schedule will vary by school and may even change week to week, and in private language schools it's quite common to work on nights, weekends, and Japanese holidays, though you'll typically get two days off each week. You'll get some personal days and other vacation days, usually more than in public schools...but read the fine print carefully. When all is said and done you probably won't be getting as much time off as they say you will. A normal working day will probably be 8-9 hours but expect your superiors to try and force/guilt you into staying later, working during your breaks, and even coming in on your off days. They might do their best to talk you out of using your vacation days as well. Chances are you'll be kept pretty busy during your working hours. You'll be teaching the classes by yourself but you'll have a curriculum to follow. Your co-workers will be a mix of foreigners and Japanese, with most of the higher ranking people likely being Japanese. If you've got decent supervisors, you'll probably do alright. If not, they could easily make your life miserable. You can find out more details about the different private school chains on various message boards online, although they tend to be dominated by complainers. Though when there's so many people saying the same bad things... Just know that some chains tend to be much better or worse than others, though in general working environments tend to be better in public schools.

Jobs in Public Schools:

The JET Program: If you want to teach in a public school, or even in Japan in general, you should first see if you can get into JET. It's a program sponsored by the Japanese government and in terms of salary, days off, and the like, it's pretty much got the best contract around. Getting into it, however, isn't all that easy. You'll need to fill out a huge application form and send it in, along with a whole bunch of other stuff at the appropriate time (generally sometime late in the year), then wait a few months in order to find out if you made it past the first round of selections (which is followed by an interview if you pass).

ALT Companies: There's a decent amount of companies that hire ALTs for various public schools who don't want to go to the trouble themselves or work with the JET Program. They're usually the best way to get into public schools if you don't make it into JET, but don't expect the contract to be anywhere near as good. You'll probably end up with a lot less money and personal/sick days. On the plus side, the application process is usually much easier than JET's and you can apply all year around (though most contracts start in April). I put links to some of them in the Useful Web Sites Section further down, but you can find more with a little bit of web searching. Most companies have a general application form on their web site that you can send in but you should also check the listings on some of the job listing sites in the Useful Web Sites section and apply directly for them as well. Applying for specific jobs instead of just to companies is a bit more work but lets you focus on just the jobs you're most interested in (elementary schools near Kyoto, for example).

Jobs in Private Language Schools:

Major School Chains: There's several large private English school chains in Japan. The biggest ones are ECC, AEON, and Berlitz. Their contracts vary a bit, as do working conditions. From what I've heard, ECC is probably the best of the bunch and Berlitz the worst. But, as I previously mentioned, it can really depend on the particular school you end up at. If you're doing some research, you'll likely run into a lot of info about Nova. They are, or rather were, the largest of the private language schools (and generally acknowledged as the worst place to work) but the company went bankrupt and fell to pieces a few years back so just ignore it. GEOS is another large language school chain that went bankrupt. Their collapse, however, was much less of a mess than Nova's and some of their schools may still be running.
Private language schools accept applications all year around, but you might be asked to travel (at your own expense) to their US office for an interview.

Small School Chains: There are many smaller private language schools as well, both single schools and small chains that only cover parts of Japan. Contracts and the like differ a lot by school so you'll have to do some research if you're looking into this route. James English School and Winbe are examples of small chains but you can find lots more by web searching and checking the afore mentioned job listing sites.

Useful Web Sites:

Public School Jobs
The JET Program
Joytalk
Interac

Private Language Schools
AEON
ECC
Berlitz
Winbe
James English School

Job Listing Sites
Japan English Teacher
ELT News
ESL Jobs Japan
Gaijin Pot

Further Information
The Teaching in Japan Page

Well, that should be enough to get you started. Keep in mind that who is accepted is a bit random and also depends on how many people that particular company needs at the time. It's best to do some research, apply to at least several places, and see which, if any give you interviews and/or offer you a position. There's a good chance that you won't get your first choice company (or even your second, third, etc) but if you're really serious about being an ALT, you'll just have to keep trying and take what you can get. Though don't think that means you have to inaccessible accept the first offer you get. If you're lucky you might get a few offers and then you can choose the best one. Once you've got all that taken care of it's time to check out So You Want to Teach English in Japan... Part 4: Things to Do Once You Get to Japan.