If the daemon is running, you can watch the event log which shows all emerging log messages.
ipfs log tail
The daemon is separated into subsystems - so does the logging. To focus it on a particular subsystem you can change the log level of the subsystem. The output shows up in the terminal where you started the daemon.
ipfs log ls
ipfs log level swarm2 info
A restart always sets the log configuration to default.
For more logging flexibility and control over its output, you must start the daemon differently.
ipfs shutdown
(ipfs daemon 2>&1) > /tmp/daemon.log
ipfs log level swarm2 info
ipfs log level dht info
Now you can watch different things in different terminals in parallel.
tail -f /tmp/daemon.out
tail -f /tmp/daemon.out | grep swarm2
tail -f /tmp/daemon.out | grep dht
Be aware of the growing /tmp/daemon.out and remove it accordingly.