"The woman says: "Yes!"."
Translation:האישה אומרת: "כן!".
Usually, ש is put if there is a clause/sentence that follows it, something like in English - The woman says that she wants to eat. האישה אומרת שהיא רוצה לאכול. If there is one word, like here, there is no need for ש. It would be like saying "The woman says that yes". It doesn't work.
Not sure how far along the course you are, but there are some general rules in different binyans, but it still comes down to memorizing.
In pa'al, if the root has three letters, like here אמר it will have ת in the feminine singular. However, there are a few exceptions, such as ישן or גדל that have ה. But there are very few verbs like that, so you just learn them.
If the root has three letters, but the third one is ה, the feminine form will stay the same, but pronounced differently, of course.
If the verb has two letters in the masculine singular form, the feminine will get ה.
Aas for other binyans, they are not as diverse. Pi'el, hitpa'el and nif'al will add ת in the feminine singular, unless the masculine ends in ה, then it's the same situation as in pa'al. The passive binyans pu'al and huf'al add only ת and hif'il only ה.