PCR is a method of replicating specific targeted portions of DNA. To perform the method you need to regulate the temperature in a very specific pattern using a thermal cycler (top left?). This will give you 'bulk' portions of your DNA.

If instead your test was just to see of your targetted portion was present real-time PCR is the method for you. It regulates the temperature like a thermal cycler but is also able to reliably determine if DNA is is being replicated very early in the cycle.

DNA sequencer (bottom left) gets you your nucleotide sequence. I'm not familiar enough with the machine to talk about how it's doing this. It really depends how much genomic info you need.

Flow cytometry is a method of detecting fluorescence on really small things, usually with fluorescently tagged antibodies involved. Say you have a test tube of cells and you want to know how many are human B cells. We can add some tagged antibody that binds B cells, then run the sample through the instrument. It has a fluid path that separates all the cells using laminar flow and then passes them by a laser. If the laser energy excites the antibody tag it will glow and the instrument can detect that light, which tells us that our antibody stuck to that cell. We can count it as a B cell. The instrument is capable of counting thousands of these events per second.

These are very generic descriptions but you can get the idea of what is happening.