It follows the lunar/Islamic calendar. It has, like the Gregorian calendar, 12 months. However, the months are either 29 days or 30 days, depending upon the moon sighting. None of the months reaches 31 days. Hence, in a year, the total days are 354 or 355, instead of 365 or 366. So, there are 10 days shorter in the Islamic calendar. In every subsequent year, an event, based upon the sighting of the moon, will take place approximately 10 days earlier, in comparison with the Gregorian calendar.
For example, this time Eid Al-Adha took place on the 20th of July. In 2022, it will take place around the 10th of July.

And Yes. Eid Ul-Fitr takes place at the end of the Month of Ramadan. That would be on the first day of the next Islamic month known as Shawwāl.