Changing your DNS is not going to help with your slow network connection. All data traffic will still use the same network; the only difference is that domain lookups (for example, the current IP address of
The New York Times - Breaking News, World News & Multimedia is 170.149.172.130) will no longer use your network's default domain name server. While this may result in a small (very small) overall improvement, the bulk of your traffic (99.99%) will not be affected in any way, shape or form.
Having said that, a simple search at play.google.com turns up several DNS change apps, many of them highly rated. Why not just try a few and be done with it?