Though dachshunds come in three coat styles, the long-haired variety is by far, the most difficult of those to maintain. This doesn't mean that it is especially difficult - the other two are just so trouble-free. However, keeping the "flag" and dust skirt of a long-hair dachshund tangle-free or at least without sticks and leaves requires a bit of concern and grooming on your part.
The first thing many think of when they consider long-haired dachshunds is the amount of shedding. It's not that short-haired dachshunds shed any less; their hair is just so very short. Additionally, the long-haired dachshund has a fluffy undercoat that sheds readily. This fine hair, not unlike that of a long haired cat, is what accumulates in the carpets and should be vacuumed out regularly.
The amount of fine hair can be kept down by somewhat regular brushings. A brushing every one or two days should keep the indoors from becoming covered in hair during the spring and summer months. Shedding slows down as soon as the winter coat is really coming in. When exactly that is depends upon your climate. In the winter, you can get by with weekly brushing unless your dog goes outdoors often.
Your dog will also appreciate the scalp treatment a combing affords. It loosens the hair and increases blood flow to the skin. Since the hair is fine on their heads and muzzles, that need only be petted for maintenance. Their backs are covered with a longer version of the slightly more coarse smooth-coated dachshund fur with a layer of the undercoat below. Their tails are made of a combination of coarse and fine fur that has grown quite long and hangs from the tail.
There is also a long section of the hair that is very fine, hanging down from the arms and sides. This hair is what requires the special attention, since it picks up just about everything. Seeds, twigs, bits of paper, leaves - even snowballs and rocks can collect there. Careful patience with a fine toothed grooming comb can remove some surprisingly stubborn mats, though regular attention should keep these from forming.
Regardless, you'll want to check your dog for attached debris whenever coming in from outdoors. Since their paws are also hairy, it's a good idea to check for stickers that may have been caught in their paw fur that rises up between your long-haired dachshund's toes.
The long-haired dachshund may be a bit more prone to developing dry skin. As such, it's not a good idea to bathe them very often, but if you must (since they're also prone to rolling into terrible, stinky and often dead things), use a high-quality, non-detergent soap. Without fragrance is best.
Just paying attention to your long-haired dachshund's fur will give you ample clues as to what sort of grooming they require. They should look shiny and feel soft.