Curriculum vita can be complicated things… they need to capture as much of your history as you can fit, without bogging down your reader with unnecessary details. Your committee might have insights on how to order your CV based on its content, but all CVs seem to include the following sections (with some variations in subsections):
1) Your training, including your prior and current professional positions (if you’re employed), your educational background, your research interests, and your fellowships & awards (although this last section sometimes gets moved elsewhere)
2) Your publications, including any peer reviewed and non-peer reviewed publications, including book reviews, as well as work that you currently have in process.
3) Your teaching experiences, which can include both courses that you’ve taught as well as classes that you’ve TAed for.
4) Your conference activities, including presentations that you’ve given and panels that you’ve helped to organize.
5) Your professional service, including any activities related to the discipline, department, or university.
6) Some people also include a section on their research experiences; this is probably only important if you’ve conducted research that isn’t reflected in your publications or interests.
How you order your CV is up to you, but its arrangement conveys implicit messages to your reader. For instance, if you’re applying for a position at a liberal arts institution, you might foreground your teaching experiences; if you’re applying for a position at a research university, you might foreground your awards and publications.
The content on your CV should be listed in reverse order, with the most recent stuff first, and oldest stuff last.
You can check out a copy of my 2011 CV here: