Whether you've just brought home a puppy or an older dog from elsewhere, your first task will be to teach her or him where to go to the bathroom other than your rugs. This is easier said than done in most cases, as the breed is very stubborn and willful. Generally, the trick is to get the dog to think that this fantastic idea is theirs.
Of course, the dachshund is also a great lover of treats, so even very small, lean treats should always be part of your training regimen. Dogs born in the Spring can often be trained with the fresh fruits of summer if they're sufficiently sweet.
The first rule of thumb is to never let them get in the habit of urinating in the house. Every single spot they smell, and rest assured, they smell them all, is an invitation to pee. Once trained up your dog should be able to resist, but until then, consider her or him to be a dangerous and loaded weapon.
Many people train dachshunds in a crate to prevent accidents like this. Otherwise, you'll need to make sure you take the puppy out every few minutes and reward them lavishly when they do go to the bathroom outside.
Unless you catch a puppy in the act of committing the misdeed in the house, there's less than no point in scolding them, as they've already forgotten what they just did. If you are unable to take the puppy out, you should keep them either in a crate or in a confined area.
Some people use paper training and swear by it. In this method, the whole of a non-carpeted room is covered in newspapers and the puppy is allowed to use the newspapers, but with some of the paper being removed each day. Eventually the paper is moved outside in the hopes that the dog will just follow the papers that you've lavishly praised her or him for eliminating upon and eventually you won't need the paper outside.
This does require a room of your house to have decreasingly large sections doused in dog urine for anywhere from 10 days to as much as three weeks. This also assumes your dog is making the connection between the urge and the act.
Crate training has the dog kept in a crate, just large enough to turn around and stand up in whenever you're not there to take the dog out. Finding the right crate for the task can be difficult, as the dachshund is a very flexible dog that tends to elongate as they grow.
By leaving the crate open while your dachshund is out, they can sometimes grow a certain fondness for sleeping or hiding out in the crate, though they much prefer the furniture if it's made available to them. Crating a dachshund puppy while you're gone, you may also avoid some of the potentially life threatening nosing around and chewing.
Either way, you should make a real plan of attack that calls for a lot of praise and a lot of you helping them not make mistakes.