Dachshunds are among the easiest dogs to travel with, as they are very portable. They're small enough to be allowed in most hotels, yet rugged enough to go camping. Even the largest standard dachshunds are able to fit in just about any car for a road trip, and they enjoy the heck out of it.
Indeed, their biggest problem when travelling is how to get enough of their head out the window for the proper "dog-in-car" experience. You'll have to train your dog very early on not to get underfoot in the car. If you don't want your dog crawling on the driver, then you'd better instill that in her or him early on, too. Otherwise, you're sure to have a dog standing on you, trying to get their head out the open window during nice weather until you reach nearly 80kph.
When staying at a hotel or motel, it is often a good idea to be particularly attentive for signs that your dog needs to go outside, as the surroundings are somewhat different. For instance, instead of scratching at the door as usual, they may simply watch the door for just a moment and then do their business right in front of it, as other dogs undoubtedly have.
You should also make a point not to leave the dog alone in a room, even if it's not forbidden by the hotel. Even if trained, dachshunds are prone to bark until released from an unfamiliar room as soon as he or she is done investigating all the nooks and crannies. Of course, barking is usually far less of a problem if the dog has been running around all day, or is somehow worn out.
The dachshund does not like flying very much at all, and nearly all show signs of anxiety when flying, such as hot and damp paws, dry nose and panting. They may also spend the entire flight crying - whether you're aware of it at the time or not depends upon where they fly. Make sure their crate is big enough to allow them to turn around and lie comfortably. Also, be sure to have plenty of fresh water and let them go to the bathroom as soon after the journey as possible.
Many dachshunds are small enough that most airlines will allow them to come on the plane with you, as long as the crate is small enough to fit under your seat. Generally, miniature and sub-miniature (tekel) dachshunds will fit under seats while the standard model usually has to be checked in the cargo hold.
Remember always that dachshunds are not to be trusted alone anywhere they could get sight of something they'd like to chase down. This means that car windows must always be up high enough to keep them from jumping out of your moving car. Also, you should be very careful of them bolting out of crate they've been confined in for any length of time.
These small precautions and arrangements are nothing compared with the joy of a dachshund out on adventure, which, with their very stout hearts, they relish above all else.