Where and how you get your DNA testing done depends on why you want to be tested. Your motives may range from necessity to curiosity. You may need a test for legal, family, or medical reasons, or you may want one to learn more about your family tree or your ancestral pedigree.
For a paternity test, if it's not to be used in court you can get a home testing kit from metaphasegenetics.com or from HomeDNA.com. Many other similar providers have sites easily found with a search engine. These tests can cost under $100. If the test is for use in court, then it will need to be witnessed and verified, which could cost a bit(maybe quite a bit)more. These kinds of tests can also reveal other family relationships.
Pre-pregnancy tests may be advisable if you or your partner think you could carry a heritable disorder such as Tay-Sachs or Cystic Fibrosis. Members of some ethnic groups prone to inherited diseases will want to get tested. You're wise to know your genetic probabilities before starting a baby. You may also want counseling as well as a test result. Go to your personal physician, or to someone your doctor refers, or find a site that offers counseling. Kimballgenetics.com is one such company, or try dnadirect.com, which offers phone counseling and personalized reports, including a report that's sent to your doctor.
DNA tests are available for genetic predispositions to disorders such as COPD, breast and ovarian cancer, and type 2 diabetes. These tests can all be found online, available from DNADirect, and from others easily found by Googling. Forewarned is forearmed.
DNA tests can also help trace your family tree. You can discover, for instance, if 2 living persons share a common ancestor. One on line provider of these kinds of tests is Kerchner's and Associates. Their informative site is at kerchner.com.
If you're purely curious about your deep ancestry, try the Genographic Project at https://www5.nationalgeographic.com/genographic. This is a project of National Geographic and IBM, designed to map the ancestry and trace the migrations of all the world's peoples. It costs about $100 to participate(which gives me pause), but it's a fascinating enterprise that promises to expand in depth and scope as time goes on.