Learn Russian: Осенняя погода плохая.

In Russian, the present tense of the verb 'to be' (like 'is', 'am', or 'are') is normally skipped. You just put the subject (погода) and its description (плохая) next to each other.

Why does осенняя end in -яя while плохая ends in -ая? Don't they both describe the same feminine noun?

Yes, they are both feminine adjectives matching погода. Плохая uses the standard hard ending -ая. However, осенняя has a soft stem (based on the word осень, which ends in a soft sign). Soft-stem adjectives use the soft ending -яя for feminine nouns instead of -ая.

How do we know плохая means 'is bad' instead of just 'bad'?

Word order is the key here. Adjectives placed before the noun usually just describe it, like осенняя погода (autumn weather). An adjective placed after the noun, like погода плохая, acts as the main point of the sentence, meaning 'the weather is bad'.

How would I use the grammar from this lesson to say 'I don't like the autumn weather'?

You would say Мне не нравится осенняя погода. Here, осенняя погода stays exactly the same (in the Nominative case) because it is the grammatical subject—the thing doing the pleasing. You just add Мне не нравится (literally 'to me is not pleasing') to the sentence.