A combination of a high alkaline product followed by an cleaning with acid should get the slate looking like new.(you should first test for acid sensitivity not only on this but all stones). This can be followed by either an impregnator to keep the natural look of the stone and to help keep the stone and grout from staining or an enhancer to bring out the color of the stone followed by an impregnator or another way is to use a topical like what is used on saltillo tile this will protect it and enhance the colors the only thing to be wary of is if there is a moisture problem it will trap moisture and cause problems.

    Steam cleaning is a term used for using an extraction method with high heat. This helps to speed up the cleaning process and makes the job easier but there are people that do just as good a job without steam cleaning it is just much more labor intensive.