There is many different ways to do this theses days and all are highly complicated. But basically what scientists do is they use small protein machinery to make copies of the DNA they want to read out, and then they use several different ways to visualise the copied DNA. This is mostly done using ingredients that have a specific color. DNA is a long string of 4 so called nucleotide bases (A, T, G and C) for each of the 4 nucleotides of DNA scientists use another color. A is green, T is blue, G is yellow and C is black, or whatever combination. The color that is visualised during the copy process allows then to recapitulate the original DNA sequence. ATGGTGGCCA would be green, blue, yellow, yellow, blue, yellow, yellow, black, black, green,…and so on. Of course it is much more complicated than this and needs very specialist machines and experts, but I hope my somewhat simplified explanation helps understanding the concept and general idea!