There are 144 DNA strands to find in the game.

They are grouped into 16 categories of each 9 unique DNA strands based on their rarity.

Once you collect 3 DNA from one of the 16 categories you will earn a reward for it. Same goes once you have collect 6 and when you have collected all 9 in the category.

Once a DNA is found first time it is collected. You can sell or use the DNA to build/upgrade a player. It will still be "collected".

You can also get more DNA strands of the same DNA. It does not matter for the discoveries. Only the first time a new DNA is found it matters here.
Getting more of the same DNA can though help you when you build a new player. See more about this in the build chamber FAQ.