Smooth Dachshunds do not require much grooming at all. They are generally free from “doggie odor” and unless they have gotten into the mud, don't need bathing very often. Wiping a Smooth Dachshund down with a wet wipe or a damp washcloth can keep him looking shiny between baths. Smooth Dachshunds shed, but not too much, so a once-per-week brushing will suffice.
Wirehaired Dachshunds, on the other hand, require regular brushing in order to keep their coats free from mats and debris, and require more frequent bathing than their smooth-coated cousins. Two to three times per year, a Wirehaired Dachshund's coat needs to be stripped, which basically involves pulling the dead hair out of the dog's body. It sounds barbaric, but a groomer can show you how to do it in a manner that will not hurt the dog.
Longhaired Dachshunds require regular bathing, and must be blow-dried in order to look their best. Daily brushing is required to keep the hair free of mats and debris.
Dachshund's ears can be prone to infection, so regular ear cleaning should be part of all grooming regimens.