What we think of as "slow internet" can sometimes be a weak WiFi signal. Wireless speeds tend to be less than wired speeds on the same network, due to interference and signal loss over distance. But there are ways you can make sure your WiFi is running as fast as possible.
Optimize your router. See #1 above.
Reduce interference from other electronics. Other devices in your home can slow down your WiFi connection, including microwaves, cordless phones, Bluetooth devices, TVs, wireless security systems, baby monitors, garage door openers, and more. If you have a newer modem, opt for a 5 GHz frequency signal to get a stronger connection and avoid some congestion from surrounding devices, many of which use the 2.4 GHz band.