Real Stone should need very little maintenance, if any. If you have a lot of dust around your place, rain usually takes care of it. Sometimes a good wash may be in order.
Manufactured Stone should also be very low maintenance, but may be more susceptible to breaking if it is struck by a hard object. It is recommended to seal manufactured stone if used on the exterior, this will help with fading, and keep the stones from absorbing water. Freeze thaw climates can be pretty harsh on concrete, so a sealer can help repel the water. Also salted driveways that get plowed can push salted slush and snow onto the stone, and salt can make the concrete to spall. So you will want to make sure this doesn’t happen.
If something gets on the stone, like acid, just rinse it really well with water. A little common sense, and you should enjoy a lifetime of maintenance free beauty!