Assuming you are running a 5.6 kernel which supports dynamic debugging, you can enable debug logs by executing:
# modprobe wireguard
# echo module wireguard +p > /sys/kernel/debug/dynamic_debug/control
The logs can than be consumed via dmesg or journalctl. With dmesg, just use following command:
$ dmesg -wH
(-H, --human enables user-friendly features like colors, relative time)
(-w, --follow)
Also on systems with systemd you can use:
$ journalctl -kf