Extended hours trading, including pre-market trading (shortly before an exchange opens) and after-market trading (shortly after an exchange closes), makes it possible for investors to stay a step ahead by performing trades outside of regular trading hours.
Trading before or after an exchange opens is handled electronically using computerized order-matching systems which are generally operated by brokers themselves, rather than by an exchange. These order-matching systems basically amount to small electronic stock exchanges on which securities are traded "over the counter".
Because extended-hour trades occur outside of exchanges, investors do not benefit from the market oversight and liquidity management which major stock exchanges provide. These and some other factors make extended hours trading more risky than regular trading.
Trades are carried out on a supply and demand basis, with no extra liquidity provided. When investors put securities up for sale during extended-hour trading sessions, the securities are not sold unless other investors on the order-matching system place orders to buy them. Orders are normally confined to limit orders, and orders expire if a buyer or seller is not found within the same extended hours trading session in which they are placed.
Not all brokers offer extended trading because it requires access to an exchange-independent electronic stock exchange with a fair amount of market participants in order to function. Of those which do, even large brokers normally place limitations on the amount of securities which can be traded before or after trading hours.
Extended-hours trading on NASDAQ is fairly popular in the United States and the United Kingdom, where the service is offered by a number of major brokers including Scottrade, TD Ameritrade, Schwab and Tradeking (as you mentioned).
In Switzerland, extended hours trading is currently offered by Julius Baer. The major private bank allows its customers to trade SMI stocks and selected Swiss mid cap stocks on its pre-market platform up to one hour before the SIX Swiss Exchange opens.