Downloading the client
The official client is available from the Google Play store for a small fee if you'd like to support the developer. It's open-source so you should be able to build your own apk to install if you prefer not to use the store, the source is available on GitHub.
There's also a fork of the Android client available on F-Droid as TTRSS-Reader.
Enable API Access
Before using the client you need to enable API access for your account in TTRSS. Make sure this is checked in the preferences page and click 'Save configuration'.
After you've installed the client, you'll need to configure the connection settings. Enter the Dark Peak URL and your credentials.
Currently two-factor auth does not work with the TTRSS-Reader client. This might be a good opportunity for an open-source contribution.