Replace Router
There's a large amount of technical jargon around Wireless Routers, such as "dual band" or "B, G and N", which don't make much sense to those without an IT degree. In short, these refer to the number of types of different signal your router can connect to. The more you have of these, the better the signal strength is likely to be as the router can switch to find the strongest one.
A good quality router doesn't need to be very expensive, and cheaper options may suit your needs more than top-of-the-range models. Discuss how you plan to use your home network at a good computer shop, being sure to mention if you plan to stream movies or use games consoles online.
Please note that not all internet providers will allow you to use your own router and will not offer technical support if you need it.