A bacterial genome consists of a large amount of DNA, usually in a single circular chromosome. Regions of the chromosome encode proteins that perform specific functions within the bacterial cell. There are two ways you can identify things that are essential. For a long time, the first approach has been the method of choice. One way that you can disrupt a bacterium's genome is with a transposon.
Transposons are pieces of DNA that can move themselves around.
When they move into a new area on the chromosome, the presence of the transposon disrupts what was there already. If you map where that disruption occurred, you now know that that region isn't essential. If you do this on a large scale you can generate a map of the regions that you can hit. If you do it on a really large scale, you start to see regions that you don't seem to be able to hit. These regions may be essential, and further experiments can be done to prove this.