Learn Spanish (Spain): Nunca me he puesto un vestido de seda.

To say you put clothing on yourself, you need the reflexive verb ponerse (to put on). Without the reflexive pronoun me, he puesto just means "I have put" or "I have placed" an object somewhere.

Is puesto an irregular verb form?

Yes, puesto is the highly irregular past participle of poner (and its reflexive form ponerse). Instead of ending in "-ido" like regular "-er" verbs, it changes completely, which is why we say me he puesto for "I have put on".

Could I put nunca at the end of the sentence instead?

Yes, but you would need to add a negative word before the verb. You can say either Nunca me he puesto... (like in this sentence) or No me he puesto nunca.... Both are perfectly natural and mean the exact same thing.

Why is it de seda instead of just putting the words together like "seda vestido"?

In Spanish, you cannot stack nouns together like we do in English to describe what something is made of. Instead, you always use the formula noun + de + material. So, a "silk dress" becomes un vestido de seda (literally "a dress of silk").