Learn Turkish: Yaz çok sıcak. - Summer is very hot.

In Turkish, there is no separate word for 'am', 'is', or 'are'. For the 'it' form (third-person singular), the meaning of 'is' is simply understood without any extra endings. You could add the factual suffix -tır to make it sıcaktır (a general fact), but in everyday speech, leaving it as sıcak is perfectly normal.

I thought yaz meant 'write'. Can it mean both?

Yes! Yaz is the noun for the season 'summer', but it is also the direct command form of the verb yazmak (to write). You will always be able to tell which one it is from the context of the sentence.

If I wanted to say 'It is hot in summer', would I still just use yaz?

No. In our sentence, summer is the subject ('Summer is very hot'), so we use the plain noun yaz. If you want to say 'in summer' or 'during summer', Turkish uses a special adverb form: yazın.

Can çok mean 'too' as well as 'very'?

Çok literally translates to 'very' or 'a lot'. However, in everyday Turkish, it is often used to mean 'too' (as in 'too hot'). If you really need to emphasize that it is excessively hot, you could use the word fazla (too much), but çok sıcak is the most natural choice for both.