Learn Russian: В апреле часто дождь.

In Russian, the present tense of the verb "to be" is almost always left out. You also do not need placeholder words like "it" or "there". The sentence literally just says "In April often rain."

Why does the dictionary word апрель become апреле here?

When you say that something happens in a specific month, you use the preposition в (in) followed by the Prepositional case. For masculine words ending in a soft sign (ь) like апрель, the ь drops off and an е is added.

Is the word дождь masculine or feminine?

It is masculine. Nouns that end in a soft sign (ь) can be either masculine or feminine in Russian, so you have to memorize their gender when you learn them.

Could I change the word order and say Дождь часто в апреле?

Yes, you can! Russian word order is very flexible. However, it is most natural to put the background information at the beginning (В апреле) and the main point or new information at the end (часто дождь).