Here's the thing: if you're on Mars, you'll be counting time in the exact same way as you do on Earth. You'll have a 24-hour day-night cycle, each hour will be 60 minutes, and each minute will be 60 seconds long. However, since 24 hours here on Earth are nothing more than the time needed for Earth to make one full rotation around its own axis, the same 24 hours on Mars happen to take slightly longer, as the Red Planet tends to rotate around itself a bit more slowly. As a result, one full day-night cycle on Mars equals 24 hours and 39.5 Earth minutes.
Now, although some of the people working at NASA are equipped with custom-built quartz watches to be able to tell what's the exact time on Mars, it looks like others prefer to rely on their trusty iPhone or Android smartphones, using a third-party app called MarsClock. The became known after a Q&A session was held on Reddit, when someone brought up the question if the NASA employees are using those special Mars watches. Here's what Surface Systems Engineer, Eric Blood, answered:
"Some of us do, but a lot of us have iPhone and Android apps with Mars time."
Well, folks, you now know what you need to do if you want to know what time it is at Curiosity's.