Yes the strength of your WiFi signal will affect your connection speeds. Wireless routers use speed throttling technology, so if they detect a weaker incoming signal link request than what they normally receive and transmit, they'll downshift to the next slower Mbp/s speed.
The only thing you can do for free is locate your wireless router closer to where you mostly hang out or at least minimize walls and interference with other signals (electromagnetic, microwave, Bluetooth, etc.). Also, the higher up the router is relative to where you are positioned, the stronger the signal will be (ie: on top of a six foot tall book case is better than being stuffed in an HDTV entertainment console two feet off the ground).