Depending on what is causing the low speed, we have several options. Let us start with a speed test to determine a general idea for how fast your internet should be. Restart your computer and close any unnecessary programs, then head over to http://www.speedtest.net/. Take a screenshot of those results, and upload so we can view them.
Now to your problem,
Is the lag only experienced while playing the game? Is the lag consistent throughout multiple servers? Are there certain times of the day when it is worse than others? How many people, if any, do you share your home internet connection with? What sort of programs are running on your computer, or rather what icons are open in the taskbar?
From here, we should be able to better isolate the source of the problem. This sort of situation is usually only caused by a handful of things; something is eating up your bandwidth on your side of the network, low connection speeds through your ISP and sometimes a connection setting is limiting speeds. Usually at least, hopefully with your answers we can narrow it down to one of these easy options.