The Naadam festival takes place every year on July 11, 12 and 13. Each city and village organizes its own festival, the largest being the one in Ulaanbaatar.
Finally, the one held in the capital is, in our opinion, the least interesting. Over the years, it has become very touristy, with tickets that are very expensive and that are practically impossible to buy in advance. We recommend instead attending the Naadams that are held in the big villages. You will thus have the opportunity to be as close as possible to the activities and even to participate in them, if you feel like it.