The short answer: two to three times a week
For most people, two or three classes a week is the sweet spot. Once a week keeps what you have; twice starts to build it; three times is where change speeds up. More than that works too, as long as you mix in lighter sessions and rest.
When you'll feel it, and when you'll see it
There's a famous line usually attributed to Joseph Pilates: in 10 sessions you'll feel the difference, in 20 you'll see it, and in 30 you'll have a new body. Take the numbers loosely, but the order is right. Body awareness and posture come first, strength next, and visible change last, depending on everything you do outside the studio.
Consistency beats intensity
Three steady weeks do more than one heroic one. Pilates works by repetition: the same patterns, done with better control each time, until your body stops needing to think about them. Missing a week isn't a problem. Stopping is.
Three simple weekly plans
Starting out: two classes, one reformer and one mat. Building: three, with reformer, mat or hot pilates, and a yoga or recovery session. Already lifting or running: one or two pilates classes as your accessory work, on days you're not training legs heavy.
The short version
Two or three a week, every week. The calendar does more than the intensity.