Apple TV + Airport Time Capsule

Hi all,
I'm just not getting this so I'm hoping someone can help.
So I have Plex installed on my iPhone, Apple TV and MacBook Pro. I recently purchased an Airport Time Capsule (TC) to be able to store my videos, photos and music, on the hope that when I'm at home I can simply connect to that TC and stream my content.
The problem is unless I have my laptop on and Plex logged in on there, Plex on my iPhone and/or Apple TV won't connect to that TC. I just get a server unavailable message.
What am I doing wrong? I just don't get it. Could someone please idiot proof this whole thing for me pleeease?
Many thanks!
James