Let's be clear about what is idiomatic:
What's the weather today? Cloudy with a chance of rain.
What's the weather like today? Cold and snowy.
Both can be used conversationally or when speaking. This is not complicated and is a beginner question, which is fine.
like is now often use here though it is not needed. like is often used in questions where the answer is a description.
- What's he like?
- He's a nice man.
Rule for questions in English with words like what, when, where, how and the verb be
The order is:
What + [is or are] [subject: the weather] today?
What is your name? Same structure.
How is your sister.
Where is your car?
How were your exams this year?
Etc. Etc. Etc.