Loose dirt and debris can scratch your fireplace if it is not removed prior to the cleaning process.
Alternatively, you can purchase a specially formulated limestone cleaner from your local hardware store to clean your limestone fireplace. Do not use soap that contains ammonia, vinegar, bleach, acids and other harsh chemicals commonly found in household cleaners to clean your limestone.
Alternatively, you can use a soft sponge, like the sponges used to wash cars, to clean the limestone.
You may use a very soft bristle brush or toothbrush to remove stubborn dirt, as well as dirt from small crevices.
Make sure to rewet your cloth in between wipes for a thorough clean.
Alternatively, you can purchase a commercial poultice from your local hardware store to remove the stains.
You can use a baby gate or another type of barrier to prevent children and pets from getting near the fireplace while the poultice is setting.
You can find soft-edged scrapers at your local hardware store. If the stains remain, then repeat steps one through three again. Try using a commercial poultice; these may be more effective.
Alternatively, you can use the vacuum to remove any remaining pieces of poultice from your limestone. Just remember to turn off the spinning brush, or remove it if it is an attachment, to avoid scratching the limestone.