The following are diseases Dobermans are prone to and the organization that conducts the test for these test:

Dilated cardiomyopathy aka DCM or Cardio

Dilated cardiomyopathy is an acquired disease that is characterized by a markedly enlarged and weakened heart muscle. In the Doberman it affects mainly the left ventricle and left atrium. It results in electrical abnormalities (irregular or abnormal or premature beats). These electrical abnormalities may result in sudden death (described below) as the very first clue of a problem in your dog. Most dogs experience symptoms of pulmonary edema with respiratory distress. DCM is observed in dogs, cats and humans, as well as a number of other species. Dilated cardiomyopathy is always rapidly fatal in Dobermans.Dobermans may manifest one of two common symptoms related to DCM. Respiratory distress, usually noted as a cough, wheeze, or labored breathing, is the most common symptom of DCM. The next common symptom is called sudden death. In sudden death owners usually observe that their dog was running in the yard then fell over and died. They are dead within a couple minutes. One third of all Dobermans destined to develop/acquire DCM will experience sudden death as the first symptom of their disease. A few dogs are noted to demonstrate a loss of stamina (also called exercise intolerance) as the main sign of DCM.
Testing done:Holter monitoring and/or Echocardiogram
Certification through:

Orthopedic Foundation for Animals (OFA) Certification can not be done until 12 months of age.

Hip Dysplasia

Hip Dysplasia is a terrible genetic disease because of the various degrees of arthritis (also called degenerative joint disease, arthrosis, osteoarthrosis) it can eventually produce, leading to pain and debilitation.

Testing done:
Radiographs of the hips

Certification through:
OFA; certification can not be done until after 24 months of age.

von Willebrand Disease aka vWD

Blood clotting disorder

Testing done:
DNA cheek swab (one time test)

Certification through:
Vet Gen

Hypothyroidism aka Thyroid

Autoimmune thyroiditis is the most common cause of primary hypothyroidism in dogs. The disease has variable onset, but tends to clinically manifest itself at 2 to 5 years of age. Dogs may be clinically normal for years, only to become hypothyroid at a later date.

Testing done:
Serum testing on T3 and T4 panels

Certification thorugh:
OFA; certification at 12 months old, should be tested yearly at 2,3,4,6, and 8 years.

Eye Testing

I couldn't fine anything on what specific eye disorder they are testing for.

Testing done:
Eyes

Certification through:
Canine Eye Registration Foundation, done yearly.
(Eye testing is especially important to white breeders since one of the claims of the DPCA is that all white Dobermans are blind or hard of seeing.)

Normally at any giving time some club somewhere is hosting a clinic that offers these test at greatly reduced rates. I will post any I find for everyone.

Certifications

There are many things out there that you can certify your dog in,
CGC is Canine Good Citizenship go to AKC.org for more information on this and many more.
TT is temperament tested: You can find info on this at American Temperament Test Society,Inc.