Usually when people ask this question, we ask them three questions. First question is, "Do you respect the Buddha?" Next question is, "Do you respect the Dhamma?" The teachings of the Buddha. The third question is, "Do you respect people who have become enlightened through the teachings of the Buddha?" If they can answer, "Yes," to all three questions then we usually say to them, "Well, you're a Buddhist."
We also go on to saying that normally Buddhists keep to a basic Morality. And try hard to make that as a practice for themselves. We may talk about the Five Precepts, basic Morality. So by respecting the Buddha, the Dhamma, the Sangha, and trying to keep to a basic Morality, undertaking the training to train in this basic Morality, then one could be a Buddhist.
"Is there a ceremony to do or something?" If one wishes to do the ceremony, then you can request what they call "Taking The Refuges," and that's actually taking refuge in the Buddha, the Dhamma, the Sangha, and the basic Morality, the Five Precepts from a monk if you wish to. It's not necessary in order to be a Buddhist, to have to do this ritual or ceremony; however, it does help many people to remind themselves of the basic Morality, that being a Buddhist means we try to follow. As well, it helps to remember to take refuge in the Buddha, the Dhamma and the Sangha. To respect the Buddha and the Dhamma and the Sangha.
Often in our normal life, it's difficult to remember to respect the Buddha, the Dhamma and the Sangha and the basic Morality. So what lay people do, is come to the monastery once a week, during the moon days, and perform this ceremony with others of the ordained Sangha, to remind themselves to respect the Buddha, the Dhamma and the Sangha, and keep to basic Morality in their normal life. Especially, if one has trouble respecting the Buddha, the Dhamma and the Sangha in one's normal life, and keeping to basic Morality, it is very helpful to do this type of ceremony and go to a Wat once a week to reconnect with the Sangha, and remind yourself what it means to be a Buddhist, a practicing Buddhist.