Forex Market is 24 hours, so you can trade anytime. However there are certain times of the day that makes trading of that particular currency pair more attractive.
Of course in the forex market governments, major international banks and large organisations are involved. I have seen some statistics that deals from these bodies are around 70% of the whole trading volume. Apart from economics and politics effect directly the currency pair, hence making the currency pair move up or down, normal deals from these bodies involve millions and millions of money. So for example, the sterling (GBP) currency do not expect it to move (hence we can profit and make money) after the London Market has closed for the day, because they have just finished their working day!
For currency pairs: EUR/USD, GBP/USD, USD/CHF
3.00AM EST – 3.00 PM EST
For currency pairs: USD/JPY, AUD/USD
00.00AM EST – 3.00PM EST
For currency pair USD / CAD
8.00AM EST – 3.00PM EST
Again you can trade anytime, but do not expect that the market will move a lot during the night for EUR/USD – just to give an example.