Some well known script automate the enumeration process.
Test them and find the one that suits you best.

linPeass : https://github.com/carlospolop/privilege-escalation-awesome-scripts-suite
LinEnum.sh : https://github.com/rebootuser/LinEnum/blob/master/LinEnum.sh
linuxprivchecker.py : https://github.com/sleventyeleven/linuxprivchecker
unixprivesc.sh : https://github.com/pentestmonkey/unix-privesc-check
lse.sh : https://github.com/diego-treitos/linux-smart-enumeration