When I'm on my period, working out is most of the time the LAST thing I want to do. While listening to your body is the most important thing, always! I know my body and if I take a week off from the gym, it is SO much harder to get back on track. So, depending on how I feel I will do the following for a workout to keep myself moving.
1) light cardio- walking on an incline on the treadmill or elliptical for 20 min
3) low intensity- lunges, kickbacks on the stair-stepper, light arms workout
4) light bike ride
What I DON'T do:
2) high intensity (ie HIIT)
Again, ALWAYS listen to YOUR body. Every body is different and what works for me is different than what will work for you. Still, if you feel up to it, make sure to push yourself a little and keep your training going. It will be worth it when you don't have to get back in the mindset of the gym the next week.
Another tip - drink extra water during this time. Your period can also be dehydrating, and extra H2O will help with bloating.