The thing is, there is no magic bullet
Your site needs to have loads of unique, valuable content to be eligible for inclusion in DMOZ. If anything, your site should not be a spam, illegal or otherwise unappealing. It has to be complete, at least.
DMOZ also says that you need to select the right category for your website to be included more quickly. So scan the DMOZ for similar sites like yours and see if the category fits you. Then apply.
Write objective description and use the company (business) name as the title (yes, no keyword stuffing unless your company name has them. Objective description means write what a passer-by would say about your site in third person. No hype or marketing speak.
By creating a valuable submission, you do the work of an editor and the editors will most likely include your site in DMOZ.
Did I say you need quality content for that?
For instance, my blog about improving websites was included with a month of the launch (I didn't notice the exact date), because (most likely) it has lots of valuable content on SEO, copywriting, usability, etc.
I suspect Old Welsh Guy's blog was included there for the same reason as well as a DMOZ editor knew him well