Learn Russian: Вчера он мылся в душе. - Yesterday he washed in the shower.

The -ся ending makes the verb reflexive, meaning the action is done to oneself. Он мылся means he washed himself. If you just used мыл without the ending, a Russian speaker would wait for you to say what he washed (like the dog or the floor)!

I learned that reflexive verbs sometimes end in -сь. Why is it -ся here?

The choice between -ся and -сь depends on the letter right before it. If the verb form ends in a consonant, like the masculine past tense мыл, you add -ся, making it мылся. If the verb form ends in a vowel, you use -сь instead.

If the subject was она (she) instead of он, how would the verb change?

In the past tense, Russian verbs must match the gender of the subject. For a female subject, the base verb becomes мыла. Since that ends in a vowel, the reflexive ending changes to -сь. So, 'she washed' would be Она мылась.

Why is the word for shower душе instead of душ?

Because it is answering the question 'where?' to indicate a location. The preposition в (in) followed by a location requires the Prepositional case. To form this case, you take the dictionary word душ and add -е to the end, giving you в душе.