If I received some BTC by accident, how would I go about contacting the person who sent it, provided I only know the sender address?
Or vice-versa like the original post, how would I contact the person who accidentally received my funds? I don't see how could I do that based only on his/her address.
Google the address, and see if it's tied to anything identifiable; some (like me) use one main address for most of their transactions, not counting associated change addresses, and you can find it tied to my profile here. Others create an address for each use, which is harder to track but not necessary impossible.
If you receive a significant amount of coins by mistake, there will likely be a post about it either here or on Reddit, or if not then any post you make is likely to be noticed by the person who lost the coins. Just make sure they sign a message with the sending bitcoin address first, to ensure it's not someone trying to scam you out of the coins!
