The best method I find is to use a good Food area Degreaser & Sanitiser, these can be bought from the usuall cleaning/Janitorial supplies. Always clean down with paper as it will remove the grease better (you are not just smearing the grease around like with a cloth) Very important it MUST be blue paper because you are working in a food safe enviroment. Finally I always dress the Stainless using a food safe oil which is designed for dressing Stainless, again can be purchased from a good supplier. A word of warning NEVER use Baby Oil, as this is NOT a food safe product.
Hope this helps
Duncan