What causes the development of antibiotic-resistant strains of bacteria?
Bacteria usually gain resistance mechanisms through horizontal gene transfer (such as conjugation and phage infection). The four main mechanisms in which bacteria elude antibiotics are:


Drug Inactivation: For example, E. coli can produce beta-lactamase that inactivate many lactam based antibiotics such as penicillin.
Alteration of Target Site: Mutations in genes encoding for target sites can reduce drug binding affinity. Example: Random mutations in DNA gyrase and topoisomerase IV reduces binding affinity to fluoroquinolone. 
Alteration of Metabolic Pathways: Many drugs target certain parts of metabolic pathways by inactivating enzymes or sequestering substrates. Bacteria can use alternative metabolic pathways or find ways to uptake the necessary nutrients from the environment.
Reduced drug accumulation: Caused by reduced drug permeability or the ability of the bacteria to transport drugs out of the cell (for example, tetA encodes for a tetracycline efflux transporter). They can gain these abilities through conjugation, phage infection (transduction), or uptake of environmental DNA (transformation).


Wikipedia has a pretty extensive and comprehensive article on antibiotic resistance. There's also a good list of references. http://en.wikipedia.org/wiki/Antibiotic_resistance