If you have an appropriate Bluetooth-compatible wireless controller (including Xbox One, PS4, and MFi controllers), you can use it with Rock Rats.
Go to your device's settings and select Bluetooth. Pair your device with the controller. Typically you press one of the buttons on the controller and then select the controller when it appears in the device settings. Check the controller's instructions for details. You should only need to pair the controller and device once. The controller will show up in the settings under General > Game Controller. You can also customize the controls there if you like, and there will be the option to add a specific customization just for Rock Rats.
When the controller is on and paired, it should automatically be detected by Rock Rats. You'll know it's detected if one of the buttons on the main menu has a yellow border. The controller should also be detected if you turn it on while Rock Rats is running.
You can use the controller to select options as well as when playing. The yellow border indicates the button that is selected. Use the direction pad's buttons to scroll through options. Press the A button to activate the selected button. (On a PS4 controller, the A button is the one with the cross.)
When playing a game, use the dpad or left thumbstick to fly (rotate, thrust forwards or backwards). Press the A button to fire and the B to jump to hyperspace (cross and circle for PS4). The X button (square on PS4) and the menu button will pause and unpause the game. When the game is paused, the A button will also continue, and B will abort the game.
If you prefer, there's an option on the settings screen to use the left trigger and right trigger for thrusting instead of the dpad or stick (those are still used for rotation). When this setting is active, previous versions of Rock Rats used A and B for thrust. To get that behavior, customize the controls under General > Game Controller to bind A and B as the triggers. Then pick whatever you like for firing and hyperspace and bind those as A and B. (Note that whatever you pick for firing will act as the menu select button.)