It is important not to let nails become long for a number of reasons. Long nails unnaturally splay the foot when the dog bears weight. Eventually, this can cause sore feet and legs and discomfort when walking or running. Long nails scratch people, furniture, and floors and will rip skin and fabric, too. And if left untended long enough, nails can grow under and into the paw, causing redness, swelling, and infection. This is undoubtedly as painful to the dog as ingrown toenails are to people. (I have seen a dog with an ingrown nail and it was not a pretty sight.)
Therefore, it is important to get a nail clipper and regularly trim the nails. Remember, too, to be patient with yourself and your dog in the process!