Learn Finnish: Se tapahtuu usein.

Not necessarily. Just like in the English phrase "it happens", the pronoun se (it) is used here to refer to a general situation or event rather than a physical thing.

Why does the verb tapahtuu end with a double vowel?

The dictionary form of the verb is tapahtua (to happen). For the "he/she/it" (third-person singular) form, you take the base stem tapahtu- and double the final vowel. Since the stem ends in u, it becomes tapahtuu.

How would I make this negative and say "It doesn't happen often"?

You would say Se ei tapahdu usein. When making it negative, you drop the doubled vowel at the end of the verb. Also, the letters ht soften to hd (tapahtuu -> tapahdu) because of a common Finnish spelling rule called consonant gradation.

Can I change the word order to Usein se tapahtuu?

Yes, you can! Finnish word order is quite flexible. Se tapahtuu usein is the standard, neutral word order. Moving usein to the beginning of the sentence simply puts more emphasis on the fact that it happens often.