Forex is open 24-hours a day. When one market closes, another one is already open in some other part of the world. However, it is a good to follow which market is open when as certain currency pairs are trading more actively than others.
There is no trading on the weekend. In Helsinki, that means no activity from 10:00 Saturday till 24:00 Sunday.
The easiest to figure out when the markets are open is to use some online tool: http://www.oanda.com/channels/forex-trader/fxmarkethours/
Be aware, that your broker might choose different trading hours - e.g. a US broker might keep closed during US holidays.
The official US timezones's current time: http://www.time.gov/.
Current time in various places: http://www.timeanddate.com/