The testing process consists of a written exam, a physical agility and two interviews. The physical agility was developed by the department, and is roughly equivalent to the CPAT (as in some candidates say it's harder than the CPAT, others say it's easier than the CPAT). The written exam, generally administered on the same day as your agility, is different depending on the position you apply for.
If you apply for a "volunteer" position (it's not truly volunteer, as you're paid hourly), the test will consist of 50 multiple choice questions, 25 Firefighter 1 and 25 EMT-B level questions. If you apply for the "duty" part time position, it will be 50 fill-in-the-blank questions.
If you pass the written and the agility, you will move on to an interview panel consisting of firefighters/paramedics. If you do well in the interview (or even if you just don't blow it), you will be recommended forward to a Chief's interview.
The Chief's interview is more of a get-to-know-you type meeting rather than a formal interview. Still, bonus points for showing up in full suit and tie for both interviews, with copies of your resume.
After all that, you'll get a conditional offer pending a background check. Our police do one of the most thorough background checks in the county, definitely more in depth than the FBI. They don't care so much what you did in your past, as long as you're open and honest about it. The background used to take a few months, but they've recently streamlined the process down to a couple weeks.