Hi BordersLass,
There are several main types of DNA tests, Y-DNA, mtDNA and autosomal DNA.
Autosomal DNA looks at all of your DNA apart from the Y chromosome (if you are male) and the mtDNA. Autosomal testing can find relatives on all your ancestral lines going back to a common ancestor about 5 generations ago. So if you have a parent that can be tested it is best to test them to maximise your chances of finding relatives. Autosomal testing will also give you an estimate of your "ethnic origin" e.g. 40% British Isles, 30% Scandinavian, 20% East Africa, 10% Mediterranean. These ethnicity estimates do need to be taken with a pinch of salt though. The test will also estimate how recently you are related, e.g. 2nd cousins, 4th cousins etc.
Autosomal testing can be done by both males and females.
Y-DNA testing can only be done by males (since only males carry a Y-chromosome) and this can trace patrilineal male line ancestors going back much further than autosomal testing can. Y-DNA testing can find relatives from around the time surnames were created and before. The Y chromosome is passed from Father to son and so should follow the inheritance of the surname (unless there was an adoption etc). With Y-testing you should find relatives who share a male line ancestor with you and get an estimate of when you share a common ancestor.
I have done autosomal and Y-DNA testing myself but not mtDNA testing but I'll try and explain what I understand about mtDNA testing.
mtDNA testing can be done by both males and females. mtDNA testing finds relatives on your Mother's direct female line; i.e. the mtDNA is only inherited from your Mother and she would have inherited it from her Mother etc. Unfortunately, from what I understand mtDNA is not as useful as autosomal or Y-DNA for family history because as the surname changes with each generation it can be very hard to work out how you are related to those that you match.
This video should help to explain testing in a bit more detail:
https://www.youtube.com/watch?v=_gmdCkH0xNIThe video is made by Maurice Gleeson and he has made some excellent DNA videos on his Youtube channel which range from basic to very advanced:
https://www.youtube.com/channel/UCcPhbETNSaXAb0I_yMGqHYgTo summarise, the only test which cannot be done by some people is the Y-DNA test which can only be done by males; however, you could get a male relative to take the test as a "proxy" for you.
I've been at the same brick with my Irish ancestors on my male line for almost 3 years now and DNA testing is slowly helping me to make progress but above all going through your DNA results and matches really is fascinating and adds a new dimension to family history research!