I’ve been there a bit and also spent a lot of time in Corsica, which is pretty similar. (search for Corsica for an idea)
In general there are lots of dirt tracks up into the mountains and down to the beaches. All great to explore. But most of the trails are either double track or goat tracks. Since the population is tiny singletrack is not well established. You will find some, but it will involve sections that are sketchy, rocky, hike-a-bike or impossible.
Local knowledge will help, but you can just go off and explore. Best times would be October through to say May. June through to Sept are bloody hot. August is way too hot to do anything.
There are some old mining tracks there which are used for mountain biking – worth speaking to Saddle Skeddadle who operate cycling tours in Sardinia.
Road biking is great there – but again, don’t bother in the summer as its just way too hot. In July I couldn’t ride my bike after about 10am or until it cooled down late in the evening.
However, scenery to die for, hills to kill you and fantastic food/drink/culture. All good.