Do they just choose an arbitrary planet and use the rotation and orbit of that planet to count the days/years? 

Do they use their home planet's date/time (even if it no longer exists)? Use an arbitrary date/time system based? Are there existing date/time systems that are not planet specific?

Lets see the problem from practical position. If I would be the space traveller without home. And possibly humanoid or about it. I need time units for: sleep-wake cycle, ship maintenance cycle and lifetime cycle.

Sleep-wake cycle is clear. Choose any value which is good for your race. For more information see [Michel Siffre][1] studies. In his experiments he live in cave for a six months and in result he has very different sleep-wake cycle.

Ship maintenance cycle - this is time for measuring ship fueling time or space travelling time. It is useful to measure it in tens-hundreds-thousands of sleep-wake cycles. On Earth we have moon cycle. It is not super precise in long-term but in ancient civilizations it was useful. As I remember on [Easter Island][2] time was measured in ["moons"][3].

Lifetime cycle - you can choose any big cycle events which you can see in space. It can be [pulsar clock][4]. From wikipedia: "However, for some millisecond pulsars, the regularity of pulsation is even more precise than an atomic clock". Or you can see [binary star][5] pulsation. Also pulsars and binary stars are not planet specific time measuring.


  [1]: https://en.wikipedia.org/wiki/Michel_Siffre
  [2]: https://en.wikipedia.org/wiki/Easter_Island
  [3]: https://en.wikipedia.org/wiki/Rapa_Nui_calendar
  [4]: https://en.wikipedia.org/wiki/Pulsar
  [5]: https://en.wikipedia.org/wiki/Binary_star