if no one else is having issues then it might be either you're machine or router.
First ping your router
hit the window button
type in cmd
type in ipconfig
look for default gateway
highlight it and copy it ( press enter )
type in ping -t then paste in your gateway with ctrl v
pay attention to the ping its its high then your having interference between you and your router
if your ping is normal goto the next step and check your internet speeds
go here to do that www.speedtest.net
if your speeds are normal ping the riot servers
similar to pinging your router you open the command prompt and type the following
ping -t 104.160.131.1
if its higher then 100 then you're having connection issues to riot, and that could be a multitude of things.