You should think about defragging your computer, I did that for TF2 when I was randomly getting slow speeds and it cleared it right up. Or it could be a number of various errors that your computer has collected over a period of time that needs to be fixed to solve slowdown.
If you want a free program that does all that for you and more, download "Advanced SystemCare 6", I use that.
If its an online game, it could just be something to do with the router, its a long shot but you could always reset your router and see if that helps.