Dachshunds are not like other dogs. Whether they are a standard or mini, they both have long backs which need support to prevent injuries. The breed is prone to IVDD (disc disease), which can cause paralysis. The main event causing paralysis is some kind of impact, like jumping or being dropped. Read this page to learn how to hold and pick up a dachshund, the right way!

[edit] Steps

Ask the owner. Before picking up any dog, make sure their owner doesn't mind you picking it up, and the dog doesn't mind being picked up. This is ok if it's your dog.
Place your hand under the Dachshund's chest. You must always support the chest.
Put your other hand around the Dachshund's rear end. Remember that you must always support the back end.
Gently lift the Dachshund up and hold close to your chest.
When you are done picking up the dachshund, set it down GENTLY. Do not "throw him down" or let him jump out of your arms, as this is one of the MAIN ways a dachshund can be injured. Bring him slowly to the ground, and gently set him down, making sure the back legs are the first to touch the ground.
If you are allowing younger children to pick up your Dachshund then supervise them with these steps or don't let them pick it up at all. If you are unsure go over them again, you have to be focused.

[edit] Tips

Be calm when picking up and holding a dachshund. If you are calm, the dog will stay relaxed.
Be gentle, take it step by step.
If the dog wants to be put down then put it down using Step 5.

[edit] Warnings

Some owners don't like people picking up their dogs.
Some dogs don't like to be picked up.
Be very careful with their backs, their discs can easily rupture and paralyze the dog.