Before you can get any job in a casino that requires you to handle money you will need to have a background check. If you have ever been arrested for any criminal activities no gamming commission anywhere in the country will license you to work in a casino.
Assuming you have a clean record you will be required to register and complete one of the many authorized casino schools. These schools can be found scattered around the USA wherever you find legal gambling, but the largest amount of them can be found in the Nevada area.
The length of the course depends on the game or games you choose to learn, but on average for one game the course can be between 50 and 100 hours, and some schools have set days for you to go to class and other schools allow a more free approach and offering revolving hours where you can show up when it is best for you and there is always classes going on for you to sit in on.
Generally the schools will offer classes for:
Pai Gow Poker
Here is an example of what you will learn in the blackjack class:
General Procedures card placement, player issues and backing up the deck
Shuffling How to Deal from the shoe
Handling and cutting the cards
Appearance, How to project a professional attitude and how to control the table
Security and maintenance
Deck, bank protection and walking the table
Hands on dealing lessons
After this it is just a matter of contacting as many different casinos as you can. There is competition for casino dealers, so you should not expect to get into one of the countries top casinos with no experience unless you have some connections. A good way to make some fast money and get some experience is to work on a cruise ship.
Many people do not like this option because you will have to share your cabin with a roommate or 2 all sharing one small room, but the rent is free and you get free meals. This is a great way to save money if you are looking to move to an area like Vegas or Atlantic City. After a few months on the ship you will have some experience and some cash in your pockets.
You should avoid moving to Vegas or Atlantic City until you have at least a year of experience as a casino dealer. There are many smaller casinos around the country many are on Indian reservations. These casinos will be able to give you a start and the experience needed to make it in the bigger casinos.
Once you have your year of experience, you can then move to one of the big casino towns. You still may not be able to get a job on the strip but you will be earning more and getting better tips. Then you can keep trying every few months and eventually you will be working in the casino of your choice dealing the game of your choice.