Can you give me a brief overview of each period`s characteristics? Let`s say i`m trying to see which period the music comes from; what would i listen for?

For Baroque, listen for an orderly kept piece. The whole piece is pretty much the same. But then again there are some abnormal weirdos.
The pianoforte existed in the Classical period, therefore people could play faster, but still not as fast as modern pianos. Some composers in between the classical and romantic periods use the pedal.
The Romantic period is very fancy, but still follows certain rules (again except for some weirdos). They are people like Chopin, Liszt, Tchaikovsky, Mendelssohn. The instruments are pretty advanced in the Romanitc period, therefore composers can do more things.
The Contemporary period is the most modern. Composers in this period do anything and everything. No one cares much about rules.

And that`s it. That was just off the top of my head. There`s lots of literature on the internet that goes in depth.

Adding to Harvey`s reply...
The ideology behind music was different in each period.
In the Baroque period, music was still considered more of a science than an art.
In the Classical period, people wanted to be entertained by it.
In the Romantic period, composers got sick of entertaining people and went in for emotional expression.
And today, there are as many ideologies as there are composers.