Okay, I'll start off first by telling you I'm a total Twitter n00b. And, I use the Twitter client, so I'll use that as my example.
With that, I'm not sure I understand your question. You want to stop people from following you or do you want to stop following others?
I don't know the answer to the first. For the second, go to your Profile (on left side of Twitter app). Then, select Following. After they load, select the name you wish to "unfollow." You'll get another window at the top of which is an "Unfollow" button. I didn't press mine as I walked through this - but I should imagine that should do it.
Again, if I've completely got your question wrong - just ignore me and I apologize. Hope I've helped, though...
Marilyn