Learn Dutch: Het zal vanavond waarschijnlijk regenen.

Because of the auxiliary verb zal (will). In Dutch, when you use an auxiliary or helping verb in the second position, the main action verb (regenen) gets pushed all the way to the end of the sentence in its full infinitive form.

Why does vanavond come before waarschijnlijk?

In Dutch sentences, words that tell us when something happens (time) usually come before words that tell us how or how likely it is (manner). So the time word vanavond (tonight) naturally comes before the probability word waarschijnlijk (probably).

How do you break down and pronounce a long word like waarschijnlijk?

It translates to probably, and it is built from waar (true), schijn (appearance), and the suffix -lijk (which works like the English -ly). A great trick to remember is that the -lijk ending is always pronounced like 'luk' in Dutch, making the whole word sound roughly like 'vahr-SCHEYN-luk'.

Could I leave out Het and just say Zal vanavond waarschijnlijk regenen?

No, just like in English, Dutch requires a dummy subject for talking about the weather. You must include Het (it), exactly as we say 'It will rain' instead of 'Will rain'.