Okay, so I just got a little multi-fx processor to muck around with, but it didn't come with its power adapter. It needs a 9V, 300mA AC adapter.

I just foolishly bought a 9V AC adapter off of ebay thinking it would be just fine, but then I realised that it runs at 850mA.

Can I still use it? Or is it gonna straight up destroy my effects unit?
I'd say just try it. There should be a fuse that'll just blow in the event of too much current. I could be completely wrong, however, and you'll end up with a destroyed FX unit. Your call
It'll be fine, just make sure the polarity is correct e.g. centre positive
How do you check the polarity? I really don't get what that is. The manual with the FX unit doesn't mention what polarity of adapter it needs.