Learn Russian: Женщины сегодня были очень заняты.

Заняты is a short-form adjective. In Russian, short forms are often used to describe temporary conditions or states. Since the women are busy specifically today (a temporary state), the short form is the standard choice here.

Женщины is feminine, so why doesn't the adjective end in -а?

Short-form adjectives agree with the noun in gender only in the singular. Because женщины (women) is plural, we must use the plural short-form ending -ы. In the plural, Russian doesn't separate genders, so заняты is used for a group of men, a group of women, or a mixed group.

If I wanted to say this in the present tense (The women are very busy today), how would the sentence change?

You would simply remove the past tense verb были (were). In the present tense, Russian drops the verb 'to be', so the sentence becomes: Женщины сегодня очень заняты. The short adjective stays exactly the same.

Does the stress change depending on the gender or number for this word?

Yes, stress in short-form adjectives often moves around! For the plural заняты, the stress is on the first syllable. But if we were talking about just one woman, it would be the feminine singular занята, where the stress jumps to the final letter.