For the kind of space travel we are performing in this day and age, time dilation effects are too small to be of much concern for mission planning. The time coordination of most space missions is synchronized to the time at the mission control. The International Space Station does its scheduling and daily routine according to Greenwich Meantime Coordinated Universal Time (UTC), updated per comments.
When you would perform space travel with relativistic speeds (note that we are entering the realm of science fiction here), you have to consider what goal you want to reach with your time-keeping. When you need to check on your fusion reactor temperature every hour, you would do so according to a conventional clock in your own reference frame, because your reactor wouldn't care about how much time has passed on Earth. But when mission control back on Earth expects hourly status reports from you, you would have to separately track the time according to Earth's frame of reference to ensure that they arrive on time. Your earth-clock would have to be aware of your current speed in earth's frame of reference so it can adjust its speed accordingly. Also keep in mind that information can only travel with the speed of light, so the earth-clock would also need to be aware of your current distance from Earth (in Earths reference frame), and add that number of light-seconds to the time it displays.
