It's offered multiple times during the year. Last summer it was offered multiple times during each week at various locations. I took mine at a Sylvan Learning Center because it was close to where I live. I couldn't imagine having to drive across town to take such an important exam. I took the NAPLEX and the MJPE 10 days apart in mid- to late July, and on August 4, I was licensed. The letter that was sent had a numerical score and then an indicator that I passed.
I don't know about other states, but I had to wait for my school to send information to the board about my intern hours before they'd allow me to sit for the exams.