Everything in this article is excellent advice! Absolutely start getting your materials together in early summer; job deadlines are getting earlier and earlier. Some schools are requesting that materials be in-hand by Oct. 1; that's an incredibly short amount of time if you start in September.
Also, when it comes to recommendation letters, it helps tremendously to have someone who can speak to your teaching skills. Talk to an advisor or a professor that you TA for; see if they would be willing to observe you several times over the course of a term. Get them to talk about your teaching strengths in their letter; it's something that can be extremely helpful in securing a job.
You'll need copies of your transcripts to send to some schools; obtain several offical copies from your undregraduate and graduate institutions so you can send them to the schools that ask for them.
Make sure that your CV is as up-to-date as possible; if you do a conference over the summer, make sure that you put the presentation on your CV before you send it out! Joe Black is also an excellent resoruce for editing CVs; he will help you streamline your CV so that it is quick to read.
Don't discount postdoctoral fellowships! They often pay really well and can be a good CV builder, as well as a good way to earn income while looking for a tenure-track position. There are some excellent ones out there. Just keep in mind that postdocs often ask for a lot more material than regular jobs, so you want to start on those applications even earlier. Postings for postdocs are often up in August and have a deadline of early October.