Oh, and if you don't have a passport, start working on that now. Click here to get started.

Adding the United States' country code (+1) to all telephone numbers listed in the document is a great way to let potential foreign employers know that you are worldly enough to acknowledge the difference in dialing numbers internationally versus domestically. It's a very small thing, and likely won't make a difference in ultimately getting the job, but it looks good.
It is also a good practice to list not only your secondary and post-secondary education (high school and college) but your primary education as well, including elementary school and junior high school. While this is not nearly as important in the American job market, the Japanese education system has given particular significance to every level of schooling. Also, your employer will want to know that you have completed all of your schooling in an English-speaking country.
Oh, and no personal references. Act like a pro; keep it professional.
After polishing our resumes, a well-worded if standardized cover letter was next. In this, basically just sell yourself like a product to your potential employers. Play up your goals and strengths, no matter how minor. Everything counts. When you're all done, just plug in the name of the school you're submitting to. Example: "I am an ideal candidate for the position of English instructor at [insert school here] because blah, blah, blah..."
Perhaps I haven't been too clear as to why standardizing your cover letter is so important. Consider this: Jessica and I contacted at least 50 schools, submitted resumes and cover letters to 40 or so of them, filled out follow-up employment applications for three of them, and were ultimately interviewed and offered jobs by only one school. Keep in mind that we were trying to get hired as a couple, which is twice as hard. Let's do the math, assuming you're trying to get a job by yourself: 50 applications, divided by the two of us. That still comes out to one job offer in 25 resumes and cover letters submitted. And finally, my point: do you really want to write 25 unique cover letters for each school you apply to, only to get one job offer? Didn't think so.
Also, many schools will request a waist-up, professional attire photograph and a scanned image of your passport I.D. page (and possibly your driver's license) with your application materials.

For us, being contacted for a Skype interview meant getting the job, as we were pretty much offered the jobs in the interview. However, this will not always be the case. If they want to interview you, then they think they want you; it's your job to prove them right.
So, now that you've been interviewed and hired, what's next? Our next step was to gather materials for our work visa application. This included 3 x 4 cm photos of our faces, color copies of our passport I.D. pages, and notarized color copies of our university diplomas (where the notary has written "This is a true copy of the original which I have sighted this date."). If you are like me and have yet to actually graduate college upon reaching this step, a signed statement from your school's registrar stating your pending graduation date, as long as it is within the visa processing time, will suffice. A degree is required for all foreign long-term visa applicants. Please note that if you are unable to have your diploma in-hand before leaving the country, a second document from your school's registrar will be required, stating that you have officially graduated and will receive your degree when it is ready. All application materials are usually sent to the hiring school, and they will submit them to immigrations on your behalf.

I hope this has been helpful. I'm always willing to answer questions if you shoot me a line. I tried to tackle the big stuff and some of the confusing stuff, but keep in mind that this is one experience. I imagine my next post will be the first from my new home in Tsukuba! Wish me luck!