Summarize:

Picking up a dachshund is different than the way you'd pick up other breeds, but it's not especially hard once you learn the right method. Start by slipping a hand under the dog's upper body to support his chest and ribcage. Don't lift up yet. Spread your fingers out so that you support as much of the dog's upper body as possible. The wider the area you can spread his weight over, the gentler it will be on his spine. Gently slip your free hand under the dog's rump — either directly behind it or just in front of the dog's rear legs to support its lower body. Get ready to lift up. Here, again, it is best to spread your hand to give the widest base of support possible. Now, simply lift the dog up. As you go, try to keep the dog's lower body from hanging or drooping beneath his lower body. A little bending is fine, but you'll want to keep the dog's back as flat as possible to keep from putting stress on it. As you move around or play with your dachshund, make sure his lower back is well-supported at all times. Dachshunds aren't like other dogs — letting their lower bodies dangle is uncomfortable to them and can contribute to painful back problems (like slipped and ruptured discs) over time. Luckily, with a little practice, this should become second nature after a while. Eventually, it will feel "wrong" to pick the dachshund up in the incorrect way. As long as the dachshund's back is well-supported and his body is fairly straight, it doesn't really matter how you choose to hold him. If you'd like the convenience of being able to hold your dachshund with one arm, try shifting to this alternate hold once you've picked him up correctly by following the steps above:  Gently shift the dog's weight so that it comes to rest on the forearm of the arm that you were using to support his rump. Use your full forearm to support his weight. Tuck the dog against your body for added support and comfort. This should feel a little like how you would cradle a baby or hold a football. Use your free arm when needed to help the dog balance and keep him from squirming or wriggling free. If you've had experience with other dog breeds, you may be used to "dropping" or gently heaving them back to the ground when you're done holding them. With dachshunds, instead, you'll want to lower the dog all the way to the ground before letting go. As always, keep his back well-supported as you lower him down. Ideally, you'll want his feet to be touching the ground before you let go. As you'll read below, even a drop of a few inches can put stress on the dachshund's back and joints.
Place one hand under the chest. Place your other hand under the dog's rump. Slowly lift the dachshund, keeping his body level. Continue to support the dog's back as you hold it. Transition to a "cradle" hold if you wish. To set the dachshund down, slowly lower him to the floor.