This is how the process worked last year:
You will receive an email indicating starting pay and emphasizing that you MUST relocate to Dallas and no relocation expenses will be paid. Are you still interested?
You will then go a few weeks without hearing a word and then they will call to set up testing. Some last time around didn't even hear back until the Friday before testing. They will fly you on down to DAL and you will take a test with around 10-20 other people. They usually have two testing groups per day, AM or PM. You will also turn in your paper application and other paperwork. You must make an 80 to pass the exam and move on to the next round.
You will get a call a day or two later indicating that you have passed the test, Congratulations! They will then invite you back down to DAL to interview. Interview consists of people department, a senior dispatcher, and the hiring manager. Last about 45 mins to an hour.
From there... you either get a call that you were hired, or you just get left hanging.