I want to connect to my time capsule using my iOS device (iPhone or iPad) and show all files from it. Please describe what should I read, how can I do this.
There is currently no native way to view files on a network share from iOS devices.
Files Connect seems to be the most feature complete of the two examples having both Google integration and Dropbox support; they even show a Time Capsule connection in their promotional image as below:
I would also think it very unlikely that any program available on an iOS device will be able to view files stored in Time Machine backups if that is one of your requirements.
Please note the links above are to the apps in UK App Store.