Hi, Elena! Believe it or not, these two questions don't actually ask the same thing: - "What is the weather today?" simply asks for the conditions. Is it sunny, cloudy, windy, rainy, etc.? We can also ask "What is today's weather?" or "What is the weather for today?" - "How is the weather today?" asks for the listener's own opinion on the weather. While the listener can answer this question the same way as "what is the weather today" by replying that it's sunny, cloudy, etc., using "how" instead of "what" also gives the listener the freedom to answer with "it's wonderful" or "it's terrible" without mentioning the actual weather conditions (if he/she so chooses). I hope this helps answer your question. Please let me know if my answer is confusing.

How is the weather today is the correct one.

What is the weather like today?