Learn Hardcore Turkish: Bugün rüzgar sert.

Turkish often drops “to be” in the present tense for third person. In sentences with an adjective or noun as the predicate, there is a zero-copula. So Bugün rüzgar sert literally says “Today wind strong,” which means “The wind is strong today.” Other examples: Hava sıcak (The weather is hot), Kapı açık (The door is open). For other tenses you do mark it: Rüzgar sertti (The wind was strong), Rüzgar sert olacak (will be strong).

Should it be serttir instead of sert?

Not in everyday speech. The suffix -dır/-dir/-dur/-dür (copular) is optional and adds formality, emphasis, or a sense of general truth. With voicing assimilation it becomes -tir after a voiceless consonant, so: sert + dir → serttir. Use it when generalizing or sounding formal:

Buralarda rüzgar genelde serttir. (Around here the wind is generally strong.)
With a time adverb like bugün, dropping it is most natural: Bugün rüzgar sert.

How can Turkish say “the wind” without an article?

Turkish has no articles. Rüzgar can mean “wind” or “the wind” depending on context. If you need to make it specific, use a demonstrative: bu rüzgar (this wind), o rüzgar (that wind).

Can I change the word order?

Yes. Common options:

Bugün rüzgar sert. (sets the time frame; the new info “strong” comes last)
Rüzgar bugün sert. (slightly more focus on the subject “the wind”)
Rüzgar sert bugün. (colloquial/marked emphasis at the end) All are grammatical; word order tweaks focus/emphasis rather than basic meaning.

Why not say Bugün rüzgar var?

Different meaning.

Bugün rüzgar var = “There is wind today / It’s windy today.”
Bugün rüzgar sert = “The wind is strong today.”
The first states the presence of wind; the second evaluates its strength.

Can I use a verb like “to blow,” e.g., esmek?

Absolutely, and it’s very natural:

Bugün rüzgar sert esiyor. (The wind is blowing hard today.)
Bugün rüzgar kuvvetli/şiddetli esiyor.
Note that adjectives can function adverbially in Turkish (no extra ending needed), so sert esiyor = “blows strongly.”

Is sert the best word here? What about kuvvetli, şiddetli, or güçlü?

All are possible, with nuances:

sert = harsh/biting (common for wind; implies unpleasant force)
kuvvetli = strong (neutral, very common: kuvvetli rüzgar)
şiddetli = severe/violent (stronger, sometimes stormy)
güçlü = powerful (understandable but less idiomatic for wind than kuvvetli in everyday speech)
Examples: Bugün rüzgar kuvvetli/şiddetli.

How do I make it negative or ask a yes/no question?

Negation of an adjectival predicate uses değil: Bugün rüzgar sert değil.
The yes/no question particle is mi/mı/mü/mu, written separately and chosen by vowel harmony: Bugün rüzgar sert mi?

Does the adjective need to agree with the subject?

No. Turkish adjectives don’t agree in number or gender. Rüzgar (singular) → sert; even with a plural subject, the adjective usually stays bare: Rüzgarlar sert (poetic/less common usage).

Do I need a suffix on bugün (like bugünde)? And how do I say “these days”?

No suffix is needed: Bugün already means “today.”
Be careful: bugün de (two words) means “today too/as well,” e.g., Bugün de rüzgar sert.
For ranges: bugünden (from today), bugüne kadar (until today).
“These days”: Bugünlerde rüzgar sert or more commonly Son günlerde / Şu sıralar rüzgar sert.

Can I say Bugün rüzgarlı to mean “It’s windy today”?

It’s understandable but sounds elliptical. More natural: Bugün hava rüzgarlı or Bugün rüzgar var. Using hava (weather) is the common pattern for such descriptions: Bugün hava güneşli/yağmurlu/rüzgarlı.

What about the spelling rüzgâr with a circumflex? How do I pronounce this word?

You’ll see both rüzgar and rüzgâr. The circumflex can mark a historically long or slightly “tense” vowel/palatalization; in modern everyday pronunciation most speakers don’t distinguish them, and the plain form is very common.
Pronunciation tips: ü is like German ü/French u (front, rounded). So rüzgar roughly: “ryuz-gar” (not “rooz-gar”).