Genetic libraries are collections of genes present in some recombinant DNA form so they can be propegated. When people refer to “screening a library” they usually have some phenotype that they are able to select or screen for and evaluate a large number of library clones to look for a gene that alters the phenotype. People interested in eukarytic biology usually make cDNA libraries that are derived from pools of mRNA isolated from an organism of interest. This allows them to isolate DNA fragments that encode proteins or RNA that are produced form the spliced form of the RNAs found in the cells. It has been a long time since I have worked with cDNA libraries, so I won’t go into that here (perhaps someone in another group can add a section?).
For example, suppose we have a strain of bacteria that can’t grow on lactose (like Salmonella) and we are interested in finding genes that are needed for lactose metabolism. First, we prepare a plasmid that has been digested with two different restriction enzymes so that is can accept similarly-digested DNA fragments. Second, we digest the genomic DNA of an organism that can metabolize lactose (like E. coli) and ligate the fragments into the plasmid. Third, we transform the Salmonella with the recombinant plasmids we have made and look for Salmonella that can grow on lactose as a carbon source. The plamsid that contains the genes responsible for lactose metabilism can then be isolated and sequenced to identify, hopefully, the lac operon of E. coli.
In the above example, a selection was used because only the cells with the ability to use lactose for food could grow. We could have also screened for the ability to cleave lactose with β-galactosidase by putting X-Gal in the plates and looking at thousands of white colonies for a blue colony
There are many variations on library creation. An investigator may choose to randomize a small segment of a cloned gene and screen the variants for a mutant with a new phenotype. A whole gene or plasmid can be mutated can be transformed for screening. A screen can be set up for “multi-copy suppressors” that rely on having an excess of a gene to obtain a phenotype. It’s all up you you and your smart noodle to figure out the best way.