Managing to get your CDL is just the first part of your truck driver training, as your CDL schooling will have taught you the barest of essentials.
New CDL drivers will almost always have to go through some type of company-training period, with an experienced trainer, to help prepare them for solo careers.
You will normally be living in the trainers truck for 3-6 weeks or so, as you learn not only the companies way of doing things, but how to handle real-world driving.
For new drivers, your training will usually be over-the-road with a trainer, but not necessarily driving as a team. Meaning rather than 1 sleep/1 drive, you may both keep the same schedules as you are trained, depending on the company.
Generally, company training will mostly be in the 3-6 week range, with some programs lasting longer.
If the training is long enough, your trainer may take home time. Every scenario is different, but generally don't expect to get home time during training, as it depends on many things such as the flow of the freight and where your trainer lives.