Learn Turkish: Ocak ve şubat çok soğuk. - January and February are very cold.

In Turkish, months and days of the week are not capitalized unless they are part of a specific, numbered date (like 14 Şubat). Ocak is only capitalized here because it is the first word of the sentence.

Where is the word for "are" in this sentence?

Turkish does not have a separate word for "to be" (am, is, are). Instead, it uses suffixes attached to the end of the sentence. For the "they" form (talking about January and February), the suffix is usually left off entirely, leaving just the adjective soğuk (cold).

Do we need to make soğuk plural since we are talking about two months?

No. In Turkish, adjectives do not change form or take plural endings to match the nouns they describe. You use the base word soğuk whether you are talking about one month or two.

Doesn't çok mean "many" or "a lot"? How does it mean "very" here?

The word çok is very flexible. When you put it before a noun, it means "a lot" or "many" (for example, çok çay means "a lot of tea"). But when you put it right before an adjective like soğuk, it means "very".