You will probably attack the problem with several solutions but in the end you should be successful. Which method you employ will probably depend on how long the stain has been sitting.
1. First of all, you can simply try scrubbing the stain with a damp cloth. If the stain is newer this can be effective. You can also try a bristle brush.
2. Secondly, you can try a masonry detergent which, as its name suggests, is a special kind of cleaning solution that is designed to work best with building supplies and materials. Follow the directions on the bottle as each product is different.
3. Third, you can try a commercial poultice, which is a mixture of ground chalk and hydrogen peroxide. Much like the detergent, different brands may alter their ingredients, which includes the substitution of active ingredients other than hydrogen peroxide.
Wet the poultice with distilled water.
Apply the poultice to the stained area.
Let it soak in for at least 48 hours. Over this time, the solution will be absorbed into the limestone.
Rinse it off.
You can also try to use other caustic solutions with things you find around the house. For instance, you might have some luck using a solution that contains vinegar and water applied to a spare or old toothbrush (instead of a bristle brush, for example).
If the limestone is outside, you can also try to use things like a pressure washer.