The most important thing to keep in mind when applying to the trucking companies is that if there's something in your past, they're probably going to find it.
You don't want to leave anything out that could be construed as trying to hide something, and many times the omission itself, rather than the item on your background check, is enough to trigger a rejection on your application.
We've set up a handy online tool that will send applications to multiple companies with one form.
Pretty much right away. You want to avoid getting your CDL and then sitting on it without driving, as most companies will want some sort of recent driving activity, even if you just got your license.
If you attend private truck driving school, then they should be able to provide you with the names of some companies that typically hire their students. Get as many pre-hire letters as possible.
Beyond that, if your past is a little more "checkered" with potential problems, you're going to want to apply to more companies, or at least companies that give a little more leeway, at least until you gain some experience.
Unfortunately, there aren't a whole lot of ways to advance your career in truck driving. Many drivers instead choose to move laterally, such as into a local truck driving job or a regional position which gets them home every weekend.
Drivers tend to simply move to other companies as their experience grows to a better paying job or one with better benefits.