Rubble masonry will need repointed over the years as the mortar joints decay. Unfortunately, rubble masonry is not quite as simple to repoint as, say, brickwork. The reason? Try using your standard pointing tool such as is used for brickwork on rubble masonry. You will quickly find that there is no standard joint thickness in rubble work. Some joints are very wide (up to 1″ was considered acceptable for rubble work historically), while others are dreadfully narrow. The joint size is dependent on the fit of the two stones. And, since rubble work does not use precise bricks of stone, the joint size will vary. This means more time and care is required to clean out and refill the joints.
Cleaning the Joints
It is tempting with tight-fitting rubble work to chisel at the stones themselves to open up a path for mortar. However, this damages the stone and does nothing to help the durability of a structure. No, the mortar and only the mortar is removed using a chisel as large or small as needed to do the job right. Go deep enough to ensure a good bond (how deep generally depends on the joint width; very wide joints will need to be cleaned out to a greater depth) or as deep as needed to reach sound mortar, whichever is deeper. This done, gently brush out the dust from the joints. This is a meticulous job, but if done right, the masonry will be preserved for many years.
Tamp Pointing
The actual pointing of rubble work is best done by tamp pointing. To tamp point, a blob of reasonably moist mortar is place on a flat surface (an upside-down trowel will work), then the mortar is literally pushed and pressed into the joint. Obviously, the mortar needs to be wet enough to penetrate into the joint, the narrower the joint; the wetter the mortar will need to be. To press the mortar in, you can use your (gloved!) fingers to shove it in, then you can even smooth out the final joint with your finger if you prefer. Or you can build a wooden tamper, and use a sliver of wood to smooth out the joint for a more professional look.

If done well, repointing can last for decades, and will provide protection to the interior mortar of a stone structure.