HA can be installed on RPi using these installation instructions:
You can search for supported devices here.
So, as an example, an integration exists for TP-Link Smart Home. You would add this integration into Home Assistant and configure it which would provide all the necessary status and control entities (see glossary) of your TP-Link devices.
Note that each integration page has links to the GitHub source code and Known Issues so that you can get more detailed information.
Also see
Integrations, add-ons and custom integrations.
There is also a Home Assistant Community Store for integrations that are not integrated into Home Assistant:
Smart phones are typically handled using the Companion App.
These forums have a wealth of information too. Here are some tips on searching for stuff here:
Tips on Searching for Answers & Duplicate Topics in the Forum.
Finally, there is The Home Assistant Cookbook - Index - a great starting point for all things Home Assistant.