CFSI and testing.
 

How many CDL test attempts do these companies that have their own training schools give you before they send you home or perhaps start charging you to re-test?
How do they work this generally?

I'm sure this will vary by company.

By the time you head in for your test, they'll have an opinion of your abilities. If your trainers feel you'll be a good fit in the company, you'll most likely get more chances then somebody who they feel doesn't have the abilities or personality they're looking for.