Yoga is one of the modalities which has been found most helpful by ME/CFS patients.
There are in-person classes, DVDs and YouTube videos which offer yoga for chronic fatigue syndrome. But it's important to pick the right type of yoga - restorative yoga is mostly floor-based (lying or sitting) and uses a lot of props to help you achieve very deep rest; restorative flow yoga takes you through a series of very slow flowing moves; and yin yoga focuses on deeper stretches for increased flexibility and gets into the parts of our bodies we don't usually stretch. You should avoid anything vigorous such as hot yoga, Bikram or Ashtanga yoga as they may will be too much for your system to cope with.
For more information about suitability see Aroga Yoga
To get you started here are some yoga practices on YouTube: