Learn Russian: Я хочу знать, как шьётся это платье.

This is the core of our current lesson! Adding -ся to an imperfective verb can give it a passive meaning. Without it, она шьёт платье means "she sews a dress" (active). By adding -ся, the object (платье) becomes the grammatical subject: платье шьётся means "the dress is being sewn." The dress isn't sewing itself; it is receiving the action.

I know the verb "to sew" is шить. Why is there a soft sign (ь) in шьётся?

Шить has a slightly irregular conjugation where a soft sign appears in the stem before the endings. For "he/she/it", the active form is шьёт. To make it passive, you simply take that third-person form and attach -ся to the very end: шьёт + ся = шьётся. You might recognize this same pattern from other short verbs like пить (пьёт) and бить (бьёт).

Could we use a perfective verb here instead of the imperfective шьётся?

No, and this is a strict rule: when you use the -ся ending to create a passive meaning, the verb must be imperfective. It focuses on the general process or an ongoing action. If you wanted to emphasize a completed result (perfective passive), Russian uses a totally different structure involving short participles, such as как сшито это платье (how this dress has been sewn).