Press "run executable" and run the installer, installing in a folder like ~/games for easy finding
If you're lucky the game now appears in bottles and you can run it, otherwise add a shortcut (button in bottles) pointing to the game's exe.
If you need controller support, from bottles click "more" on the game and add it to steam (restart steam for it to show up) and launch the game from steam and it will take care of the controller mapping and you even get the nice remapping features.
Bottles provides some installers but for example with fitgirl repacks I heavily recommend letting the fitgirl installer install redists.
Another option is to manually download your redist and run it through the same "run executable" as before. Bottles is a program for managing several "wine bottles" (get it?) And a single bottle is like a single windows install (in real terms, this is what a "wine prefix" is), so a program installed in a bottle is a program that is visible to other programs in that bottle. For example, if you install Titanfall in bottles, you can then use the third-party Titanfall modded launchers as you would do on windows.
Some desktop programs (dnspy is the one that caused me problems personally) can be incompatible with the bottles setting, so for these programs specifically you should create a new bottle with the settings that work. Most of the time, this involves disabling DXVK for that bottle.