This is what I get when starting airodump-ng
root@guido-laptop:/home/guido# airodump-ng wlan0
ioctl(SIOCSIWMODE) failed: Device or resource busy
ARP linktype is set to 1 (Ethernet) - expected ARPHRD_IEEE80211,
ARPHRD_IEEE80211_FULL or ARPHRD_IEEE80211_PRISM instead. Make
sure RFMON is enabled: run 'airmon-ng start wlan0 <#>'
Sysfs injection support was not found either.
sudo stop network-manager
)? Try again after that and if that still fails, follow the suggestion in the error message you posted.