In the type of work that we do, just getting the cells out of the rock or sediment where they were living can be difficult. Many of these organisms are adapted to live at high temperatures and pressures, and live deeply embedded in rock and aren't going to detach just because we scientists want them to. There are chemicals that help with this step as well as various regimes of shaking, spinning, heating and cooling. From there the next step is to lyse (burst) the cells so that they release their DNA (or RNA depending on what you are interested in). This can be accomplished with freezing and thawing as well as sonication (using sound to move particles), and more chemicals. When a cell bursts it releases more than just DNA, and so the next step is to use other chemicals to make sure that the cells' own enzymes don't break down the DNA (or RNA) that we are interested in. If there are lots of metals present in the sample they need to be removed with still other chemicals. Eventually you have (hopefully) isolated your DNA and you are ready to make copies of it so that you have enough to "read". One way this is done is with a PCR (polymerase chain reaction). In a tiny tube goes your DNA, loose nucleotides (raw material to make more DNA), an enzyme (does the actual assembly), primers (tell the enzyme where to start and stop building), water and buffer. Then the tubes are placed in a machine that runs them through cycles of heat and cold to (hopefully) stimulate the enzyme to make copies of the DNA by assembling the nucleotides in the same order they are assembled in the original DNA.
Lots of things can (and do) go wrong in this process. If you didn't have DNA to begin with, you will get no DNA after the PCR (obviously). If you use the wrong primers they won't match up with the DNA, and the process can't start. If the temperature is too hot or too cold, the enzyme makes mistakes and copies the DNA incorrectly or doesn't work at all. If there are too many metals in the solution left over from the sediment, the reaction will not work. If your enzyme has been stored incorrectly it will not work. When it doesn't work you simply try again, and again, and again until you figure out which step went wrong. Keep in mind that this has to happen for each sample you are dealing with.
Once you have your PCR product (amplified segments of DNA selected by your primers), it gets run on an electrophoresis gel. Basically you use electricity to move the DNA segments through a gel (kind of like gelatin). The smallest fragments will be pushed the farthest along the gel by the electricity and the largest fragments will move the least. If all goes according to plans, you see bands in the gel corresponding to different-sized fragments of DNA. Each band represents millions of copies of that specific fragment. At that point you use a gel extraction kit to remove the now-purified (all the same segment) DNA from the gel. At this point the DNA gets sent off for sequencing where various technologies that are too technical for this blog (maybe I'll try explaining when I understand them better... on the other hand, maybe I'll spare you that) are used to read the pattern of A's, C's, T's, and G's of each fragment. The code then gets sent back to the scientists who have to figure out how to assemble the various fragments of DNA into something that can be useful.
The final step is analysis. Depending on the question asked, this might be trying to use the genetic code to figure out how closely related two species are, or what organisms were in your sample, or what genes were present, or any one of a number of different questions. For each question there are multiple ways to search for an answer and in some cases different methods will provide different answers. Scientists need to understand the (often new) technologies used for the various steps so that they can properly interpret the data. It is not enough to simple know the code. A question as simple as "is species A more closely related to species B or species C?" can have different answers depending on what part of the DNA was amplified. Sometimes one gene can tell one evolutionary story, where a whole genome (all the DNA in an organism) can tell a very different one. If you only look at the one gene, you might never know. This is why scientists still argue about how certain species evolved and why phylogenetic trees (think family tree of species based on genetics) can be very controversial.
The point is not that science is hard (duh!), or even to make you think I am crazy for wanting to do all of this. However, maybe next time you watch CSI or Law and Order and the crime lab instantaneously delivers that key DNA evidence, you will realize that science doesn't actually work that fast, and you will know that it really is quite complicated!