Serious question here: how do they get ancient DNA from dried up bones?

I did a Living DNA test a while back and it said my (mitochondrial) maternal haplogroup B2 was 24% from the United States.
The rest of the "shared mitochondrial DNA" breakdown was thus:
China 20.6%
South Korea 20.2%
North Korea 20.2%
Philippines 9.5%
Khamnigan 7.1%
Kyrgyzstan 7.9%
Mongolia 8.4%
Taiwan 6.8%
Uyghur 7.3%
Khakassia 6.4%
Tuvinian 6.8%
Altai 6.4%
Tibet 4.7%
Kalmyk 3.6%
Buryat 4.3%
Kazakhstan 3.3%
Ainu 2.0%
Yakut 1.4%
Japan 2.1%
Uzbekistan 1.4%
Turkmenistan 1.1%

I wanted to get my dad's side done, but my brother sent in a sample that they said wasn't sufficient and then he died before he could send in another sample. If they couldn't get a good enough sample from my living brother, how do they get good enough samples from dead people?