By default, zcashd logs to ~/.zcash/testnet3/debug.log when running on testnet. To output to console, run zcashd -printtoconsole or set printtoconsole=1 in your zcash.conf.
Also useful: -debug=[STRING] to log certain debug info. For miners, -debug=pow can be useful to get an idea of what is going in (although it is of course inefficient to leave that enabled full-time).