One of the major criticisms of Ezine Articles is that they take so long to review and accept your articles. This is definitely true at the start, when it can take a week or more to see your article go live. But the process speeds up a lot after they've accepted 10 articles from you. It usually takes a couple of days, maybe a bit more once you've reached that number.
And what I've found is that when you've written quite a few more than that, the process speeds up even more. I've got over 30 articles on the site and most of the ones I've been submitting lately are being accepted within 24-48 hours. I might just have been lucky lately, but I don't think so. I suspect that there is a bit of fast-tracking for people who have that many up or more.
So, my advice is: Only submit good articles that are grammatically correct and have been thoroughly spell-checked. Also, be careful to observe their link rules (see the site for details). Then be patient and cooperative. And just keep submitting your best work to them.
This is worth doing because articles there do get a lot of views, and deliver strong SEO benefits to sites they link back to in the author bio-box.