I'm trying to put a list of ancestors that my mom had been compiling before her death in 2008. I'm new at this. She had all the documentation and trees in a database on her computer. All was lost while my father was in a hurry to move on. I did find the list. Cheney is on her list, but ended with Richard.. My mom has other lines up to king Edward II - I know I've seen post that no one in USA can be traced. You mentioned DNA (I know what it is) but how exactly does it prove or disprove? If I go by her list this would be my dads 10 generation & on another line king edward is 21@ great grandparents
The best advice I can give you is to start with yourself (and any siblings) and your parents, and work backward as far as you can. The US Censuses are a surprising amount of help in this, back to 1850 - beyond that it gets harder.
Since the Cheneys ARE relatives of Former VP Dick Cheney (it's been confirmed), they come under more than usual suspicion and require more cross-checking than usual. I wouldn't put it past Tricky Dick to make exorbitant claims for his ancestry that...may not be in strict accordance with the truth.
Regarding DNA, it's of limited use. MtDNA can only track female-to-female lines, Y-DNA can only track male-to-male lines, and both of them depend *very* heavily on volunteers, documentation, and the relative rarity of the haplotype. Autosomal DNA won't tell you much past three to five generations - the "signal to noise ratio" gets too garbled.
Due to family circumstances (not connected with the lines under discussion), I was able to confirm that my direct-line male ancestry was not only German, but from a particular area in Germany. However, that still didn't identify exactly which residents were my direct ancestors, because of missing documentation links.