Trucking companies will sponsor you by paying for your CDL schooling and on-the-road training with them. In return you agree to drive for them for a specific amount of time or miles. This agreement will be spelled out in a legally-binding contract.
Most companies will require about a one year commitment to them. As a general rule, new drivers will want to keep their first job for a year, anyhow, as many companies will require at least that much experience should you want to move on.
Leaving the company before your commitment has been satisfied may require you to pay back some, or even all, of the training costs to the company. It may also prevent you from driving for another company until that debt has been paid in full.
In some cases, trucking companies may require an applicant to reside in a specific state or region, or within a certain distance of a terminal. Most of the larger companies, however, will not normally have those restrictions.
Generally, most drivers in most states should have no issues. The FMCSA rules are set up as such that drivers who test in one state can transfer the results to their state of domicile or residence. There are exceptions, so drivers will need to verify their state rules.
Company-sponsored training will be short & swift compared to private school. They both give the basics needed to pass the CDL test, but companies may be in a hurry to get the driver into the trainers truck and get it moving.
No, the trucking company will foot the bill for that, as well. Most will have them travel by Greyhound bus, though there are reports of a few companies paying for plane tickets for drivers to travel to training.
Drivers are usually free to provide their own transportation to training, but it's not necessary.
In most cases, once you get your CDL, the company will match you up with a driver-trainer. The trainer will either team-drive with you (one sleeps, one drives), or train you from the front seat, with both of you keeping the same sleep schedules. Most training will be over-the-road, so most students will need to go to training prepared to leave immediately after testing.
In some cases, drivers may have to wait a week or more at the facility, or even from home occasionally, until a trainer becomes available.
In most cases, new drivers will be obligated to the trucking company for either a specific period of time, or number of miles driven, though every company handles it differently.
Some companies will require a certain amount of time, like a year. Some will consider your obligation fulfilled after a certain number of miles. Some will deduct a certain amount of the cost of tuition and training for every month driven. It just depends on the company.