You pay for the time you fly.
Well, that might or might not be entirely true, depending on the exact setup of the school/club.
When I learned to fly in Florida the lessons were scheduled in two-hour blocks. In such a two-hour block you would fly approximately one hour, and had another hour with the instructor for pre- and post flight briefings, preflight and so forth. Once I got to the x-country stage, the blocks became progressively larger of course. The total charge (airplane plus instructor) was based on hobbs time, so if we flew only 54 minutes, the hobbs would read 0.9 and I paid for 0.9 hours. Additionally, there was a set charge per hour one-on-one groundschool if you needed that.
At the club where I now fly we have freelance instructors. Lessons are again scheduled in two-hours blocks (by default, but that can be changed if required). The instructor is paid a fixed amount of money for his time, regardless of whether that's flying, briefings or ground school. So you pay the instructor for two hours if you booked a two-hour block. Easy. Furthermore, the aircraft are paid based on tacho or hobbs time (depends on the aircraft). So for a typical lesson you pay the instructor for two hours, and the aircraft for one hour.
But in any case, all this should have been made clear to you at the start of your first proper lesson so you know what to expect. In fact, both the school in Florida I went to, and my current club, will give each new student a talk-through of all the charges they can expect during their training, and how these charges are calculated.