Learn Romanian: Cerul este înnorat astăzi.

In Romanian, the definite article (meaning 'the') attaches to the end of the noun. Cer means sky and is a neuter noun. To say 'the sky', you add the singular neuter ending -ul, making it cerul.

I recognize the word nor (cloud) inside înnorat. How does this word building work?

You spotted it! You can often turn a noun into an adjective describing a state by adding the prefix în- and the suffix -at. So nor (cloud) becomes înnorat (cloudy).

Could I use azi instead of astăzi in this sentence?

Yes, absolutely. Azi and astăzi both mean 'today' and are interchangeable. Astăzi is just a slightly longer, slightly more formal version of the same word.

Would the ending of înnorat change if we were describing a feminine noun?

Yes. Because cer is a neuter noun, it acts like a masculine noun in the singular, so we use the base masculine/neuter form înnorat. If you were describing a feminine noun, you would add an -ă at the end, making it înnorată.