Forex market is open 24 hours a day, five days a week. You can make money in the forex when the market moves up, and you can even make money when the market moves down.  However, you will have a very difficult time trying to make money when the market doesn’t move at all. 
Before looking at the best times to trade, we must look at what a 24hr. day in the forex world looks like.  The forex can be broken up into three major trading sessions:  the Tokyo Session, the London Session, and the U.S. Session. The international currency market isn't dominated by a single market exchange but involves a global network of exchanges and brokers around the world. Forex trading hours are based on when trading is open in each participating country:

New York 8am to 5pm EST
Tokyo 7pm to 4am EST
Sydney 5pm to 2am EST
London 3am to 12 noon EST

At times when markets overlap, the highest volume of trades occurs.
If you need to know the exact times that the markets open and close, you have to take time zones into consideration. It is very simple when expressed in UTC. This is Universal Coordinated Time, formerly known as Greenwich Mean Time. This is the standard (winter) time in Greenwich, London which is the point of zero longitude on the globe.
So, the normal forex market hours are 22.00 Sunday UTC to 22.00 Friday UTC. This is 10 pm in the UK in winter time.
New York is 5 hours behind the UK so the global forex market opens and closes at 5 pm Sunday/Friday in New York, 2 pm on the US west coast, 11 pm in Germany, 8 am Monday/Saturday in Sydney.
Things get a little complicated when you start to try to take summer time daylight saving into account. This makes one hour difference in countries that observe it. But daylight saving operates in a different way in the southern hemisphere countries such as Australia which have summer time from September to March instead of March to September.
The hours of the different major national markets are as follows:

Sydney: 10 pm to 7 am UTC
Tokyo: 12 midnight to 9 am UTC
London: 8 am to 5 pm UTC
New York: 1 pm to 10 pm UTC

Or we can express that in EST (Eastern US time):

Sydney: 5 pm to 2 am EST
Tokyo: 7 pm to 4 am EST
London: 3 am to 12 noon EST
New York: 8 am to 5 pm EST

You can see that these correspond to 24 hour cover.

However, this does not necessarily mean that trading will be good at all of these times. Just after a major market opens, the prices can be very volatile and unpredictable. Many traders will stay out of the forex market for up to an hour four times a day when the financial markets are waking up in these major cities.

The US dollar is the most traded currency by a long way, involved in 2.5 times as many trades as its nearest rival the euro. This means that events in the USA have a greater impact on the financial markets than events in other countries. The New York market tends to slow down around 3 pm local time (8 pm UTC) and if you are involved in a US dollar pair, this can be a good time to stop trading for the day.
So theoretically you can trade 24 hours a day from Sunday night to Friday night. But clearly, it is almost humanly impossible for you and I to stay up 24 hours a day to trade.
Never fear as automated software in the form of a forex robot can even make this physically possible. However, a cautious trader will choose his times and will not be active during all of the Forex market hours.