Like Pahoo says, 'cloudy white' can be a lot of things. I'd start with any wood soap and clean it first. Murphy's Oil Soap, for example.
"...by Pledge..." Isn't as daft as it sounds. Wood is wood. Use the same products and techniques used on fine furniture. None of which is horribly expensive. Think water stain from somebody putting their beer on a wood coffee table.
Mind you, a lot will depend on what finish is on it now. If somebody lost their mind and slathered polyurethane on it, that's plastic and gets treated differently.