This may be an oversimplification, but truly, it's the best answer I have for this.
Moral Law deals with our relationship to God and to our fellow man. Moral law can all be traced back to Matthew 22:36-40 (NIV quoted below)
36 “Teacher, which is the greatest commandment in the Law?”
37 Jesus replied: “‘Love the Lord your God with all your heart and
with all your soul and with all your mind.’[a] 38 This is the first
and greatest commandment. 39 And the second is like it: ‘Love your
neighbor as yourself.’[b] 40 All the Law and the Prophets hang on
these two commandments.”
Take any of the laws and trace it back to the obvious purpose, and you can see what is moral law, what is civil law, and what is ceremonial law.
the Ten commandments, including thou shalt not Kill, thou shalt not steal, thou shalt not covet... All of these have to do with showing love toward our fellow people. If we love someone we will not kill them, steal from them, or covet their things. If we love God, we will have no other gods before Him, we will not bow down to idols.
Civil law deals with things like establishment of guilt, proper punishment for offenses. It's easily recognizable as similar to our own civil laws.
Ceremonial law would include such things as the dimensions of the temple, the colors of the robes for certain priests, etc.