Tú (with accent mark) is a subject pronoun. It's used to say who is doing the action. Often, the subject is unnecessary in Spanish, since the ending on the verb gives it away. This is the case in this sentence.
Tu (no accent) is a possessive pronoun, translating to "your" in English. It is used to say that something belongs to you.
Te is an object pronoun. It represents the direct object, indirect object, or reflexive object.
- I love you. (Yo) te quiero. (direct object)
- He gives you the gift. (Él) te da el regalo. (indirect object)
- Are you taking a shower? ¿(Tú) te duchas? (reflexive object)
In this sentence, the "te" is a reflexive pronoun as part of the verb "ponerse" (to put on).
Reflexive verb: ponerse - to put on
Learn the conjugation:
(Yo) me pongo
(tú) te pones
(él/ella) se pone
(nosotros, nosotras) nos ponemos
(ustedes) se ponen
(ellos/ellas) se ponen
Why not ponerse? If I say ¿Ella ponerse el vestido nuevo? How is that different?
You're using the verb in its infinitive form there. It would be like saying "She to put on the new dress" in English.