This may be an incredibly simple question, but I am just getting started.

I was recently given a juniper bonsai as a gift. I started reading about how to care for it, and I learn it is an outdoor tree. Fair enough; I put it on my balcony. But then I also read that overwatering can be a serious problem for the tree. I live in an area with fairly frequent and heavy rainstorms. Is that going to amount to overatering? And if so is there any way I can both keep the tree outside and not drown it?

Yes, the answer is dual: 1) check your tree daily, and react to what you see, and 2) make sure you repot in a good open substrate.
Remember that in nature treses also receive lots of rain sometimes and don't drown, but ( big but) they do not live in a container with poor drainage and/ or clogged soil

Main concern is to have the soil soaking wet for a long period of time. So in fall you have to be carefull. Just normal summer rainstorms are no issue for established plants.