How old is your dog?
What breed is your dog?
Shaking or trembling in small breeds at a young age could be due to hypoglycemia, liver shunt, or a neurologic response such as a seizure. Trembling can also be a sign of pain, stress and cold.
Hypoglycemia is low blood sugar and frequently causing trembling in small breeds. Feeding your dog smaller meals more frequently can help. If you suspect your dog is having low blood sugar you can put a drop of pancake syrup on your dog's tongue which should raise the level. http://www.petplace.com/dogs/hypoglycemia-in-dogs/page1.aspx
A liver shunt is usually a genetic condition. It is a condition where instead of the blood going through the liver and being cleansed, part of the blood is diverted around the liver resulting in a toxic buildup in the blood. You can read about these here: http://www.malteseonly.com/shunt2.html
Seizures can manifest as trembling and a dog may not lose conscienceness. You can read more about seizures here: http://www.marvistavet.com/html/body_seizure_disorder.html
Being a dachshund beagle mix, I would also suspect a possible back injury since both breeds are known to have disc issues. These issues would lead to pain and trembling. You can read about this here:http://www.petplace.com/dogs/intervertebral-disc-disease-thoracolumbar-area-in-dogs/page1.aspx http://www.petplace.com/dogs/intervertebral-disc-disease-cervical-area/page1.aspx
Buffered aspirin can be given to a dog with a dosage of up to 5-10 mg per pound every 12 hours. Keep in mind that a dog's body does not metabolize aspirin in the same way as a human and thus should not be given more than a day or two without contacting your Vet. Read side effects and precautions here.http://www.petplace.com/drug-library/acetylsalicylic-acid-aspirin/page1.aspx
You will want to have your dog seen by your Vet to be evaluated and discuss treatment options.
Hope this helps.