Search international listings for jobs in your area of specialization. Remember that an international job search, unlike a United States one, is year-round; just as the United States job market winds down for the year, the Australian and New Zealand ones, for example, pick up momentum.
Solicit reference letters. You should have letters from your adviser and a few members of your dissertation committee if you are a new PhD. If you are employed, you need at least one letter from someone at your current university. Letters from people outside your PhD institution and current job demonstrate breadth of professional network. Letters from people outside the United States are important in an international search.
Prepare CVs in the standard format required by the countries to which you are applying. Remember that each country has its own preferred CV format. Include explanatory notes about United States institutions and teaching. Search committees outside the United States may not be familiar with any but the most distinguished United States universities and cannot be expected to know United States curricula. Rather than say "senior seminar," for example, explain "a 16-week long fourth-year course meeting three hours a week, in which students were assessed by three substantial essays graded by the instructor."
Fill out application forms, being especially carefully to show how each element of your academic experience conforms the criteria specified in the job posting. For many countries, initial screening is done by human resources staff verifying checklists. Do not assume, for example, that a line on your CV describing a teaching assistantship will automatically be evaluated as "experience assessing student exam scripts;" you need to make the connection explicitly for the staff reading the application.
Do your research. Make a habit of reading higher education journals such as "The Chronicle of Higher Education" and "The Times Higher Education Supplement." Keep up with philosophy blogs, list-serves and wikis, as well as research journals.