If your on a wifi connection and it's open, people could be sipping your bandwidth up. If your wifi is open, you can access your routers homepage (usually 192.168.1.1), now comes the hard part. Opening up your routers homepage will prompt you with a username & password. Generally the default UN and PW are admin & admin respectively, but it varies from brand name routers. Unless you already know the UN & PW, you need to provide us the router model so we can help.
If you are able to log in, your going to want to put up a password for your wifi. I advise against using a WEP password, it's absolete and easily cracked. What you want is a WPA or WPA2 if your router supports it.
If your issues are on a wired connection, then your problem isn't so simple.