How to set any controller to use the original PS2 controls

In the top left of the main Steam application window, click the Steam menu button and click Settings from the menu.

In the Settings menu window, click Controller and then General Controller Settings

Doing so will open a separate window with the Big Picture interface. Steam has built in support for the big 3 controller manufacturers - Nintendo, Microsoft, and Sony, as well as Generic gamepad configuration (which covers things like Logitechs or 8bitdos) You can enable them all without it causing any issues, but at the very least, make sure to enable every relevant option for the type of controller you are using.

In addition to universally enabling or disabling controller support altogether, and enabling or disabling specific manufacturer support, you can customize controller configurations for each individual game.

To edit the controller settings for GTA: San Andreas specifically, right click on the thumbnail in your library for GTA San Andreas and click Properties on the context menu.

Click on Controller along the left side.

If it is not already selected, click on Enable Steam Input in the dropdown box. Underneath the drop-down, all of the enabled controller support methods will be displayed from the previous section of the guide.

Next you'll have to actually go in to Big Picture mode for further customization

Open big picture mode using the icon in the upper right of your Steam desktop application.

Navigate to the Library section.

Select San Andreas.

Click Manage Game.

Generally people are going to name their config something logical. We're looking for the PS2 controls.

Click on "Original PS2 Controls for GTA: San Andreas.

Click on Apply Configuration and enjoy the game the way it was meant to be played.