It really depends. Honestly, each of the ones you listed have separate requirements and/or unions (with the exception of the usher and ticket taker; they are the same union).
For instance, I am a floor director/backup ticket taker for my theatre and I got the job because I previously worked in concessions for the same theatre and the house manager knew who I was. So, in that case, it was all about who you know. To work in concessions though, I applied for that job when it was posted on Playbill.
Almost all of the jobs you are inquiring about are covered by a union (unless something has changed, concessions is not covered by a union, nor is merchandise). Each of those unions will have their own requirements in order to join: i.e the ushers union requires you work a minimum number of performances before you can join the union and if you want to continue to usher, at that point you will have to.
Also, just so you are aware, the people who work in the box office are generally called Box Office Treasurers (or Assistant Box Office Treasurers, etc).
If there is a career in particular you are interested in, my advice would be to contact their union and speak with someone who can go through the requirements with you and get you started on your path to working in the industry!