Learn Russian: Мой брат хочет танцевать.

Just like in English ("wants to dance"), when you use a verb like хотеть (to want) or мочь (can/to be able to), the second verb stays in its dictionary form (the infinitive). The first verb (хочет) changes to match the person doing the action, which is "my brother" here, and the second verb (танцевать) just names the action.

How do I conjugate хотеть for other pronouns like "I" or "they"?

Хотеть is a very useful but slightly unusual verb! In the singular, it takes "e" endings: я хочу (I want), ты хочешь (you want), он/она хочет (he/she wants). But in the plural, it switches to "i" endings: мы хотим (we want), вы хотите (you all want), они хотят (they want).

Why do we use Мой for "my" in this sentence?

Words like "my" must match the gender of the noun they describe. Because брат (brother) is a masculine noun, we use the masculine form Мой. If the sentence was about a sister, you would need the feminine form: Моя сестра хочет танцевать.

Can I change the word order to: Мой брат танцевать хочет?

Yes, because Russian word order is very flexible! While Subject-Verb-Infinitive (Мой брат хочет танцевать) is the most neutral and common order, you could put хочет at the end. However, doing that usually puts special emotional emphasis on the word at the end, making it sound more like "My brother DOES want to dance." For normal statements, stick to the order in this example.