It begins with the submission of your application, I went through an employee referral so I don't know if this is done online, although I'm sure it is. The next step is you do a phone interview with a recruiter, they ask you basic questions, I had some industry experience already so my questions was mostly based on my knowledge of the industry. Once you pass that process you take two test at a UBS location. They are web based, and timed, one test is problem solving based, the other is more mathematical. The purpose is to determine if you have the capacity to pass the series 7. Once you pass the test you do another phone interview (same recruiter as before), behavior based questions, then they do a background check, drug test.
If you pass all that then they fly you and the other recruits to the market area HQ for two days of interviews. After that you find out if your in the program or not.