Implement UI buttons in Input Manager

Where you have your if(Input... code with a UI button you just create a script and have a public function e.g.

 public void MoveRight()
 {
     // depending on you game do the move code here
     // or set a bool to true moveMeRight = true and in Update
     // if(moveMeRight)
     //      Do your code here
 }

Then drag that script onto your button, highlight the button and click + in the OnClick area.

A slot appears so drag your button onto it, the button contains the script so in the dropdown select MyScriptName -> MoveRight

You might want different functionality than a click though so you can also Add Component -> Event Trigger

From there you could add a PointerDown event to set that bool I mentioned and PointerUp that calls another function in that script called StopRight to set the bool to false. That way you keep moving right until you lift the pointer.