I understand bacteria have become resistant to antibiotics due to selection pressures, but how do resistant bacteria process antibiotics when exposed to it, compared to non-resistant bacteria. Also, what research is being conducted to combat bacteria resistant to antibiotics?
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:
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
You've gotten some decent answers for how antibiotic resistance arises, so I thought I'd touch on this a bit. There's three major thrusts to anti-resistance research:
The lead question you have answered yourself: bacteria become resistant because of the selection pressure caused by the antibiotic's effective suppression of the original non-resistant bacteria. Those variants which resist the suppression are selected for as a natural consequence.
How do resistant bacteria process antibiotics? It depends on the details of the particular antibiotic, and perhaps the kind of resistance.
Take the case of penicillin and related antibiotics, like amoxicillin. These antibiotics act by inhibiting the formation of a layer of the cell wall which is essential for many kinds of bacteria. This prevents multiplication of the bacteria and contributes to their distruction. Wikipedia gives some details on the action of these β-lactam antibiotics.
Bacterial resistance to drugs like penicillin usually takes the form of the bacteria producing an enzyme (called β-lactamase) which breaks apart a ring in the drug molecule, disabling it and thus removing its effect on cell wall synthesis.
This resistance has become common because of the widespread use of penicillin-like drugs and because of transfer of the gene for it between bacteria species as by plasmids.
Researchers managed in the 70s to discover and develop an auxilliary weapon in this war. This was clavulanic acid, which has a structure partly similar to the penicillins and like them is attacked by the bacterial β-lactamase enzyme. Unlike the penicilins though, it forms a permanent bond with the enzyme molecule, disabling its activity. This has led to currently effective drugs like Augmentin which include in the same pill both amoxicillin and its protector, clavulanic acid.
Most resistance is acquired by horizontal transfer by various means
Conjugation is the sexual transfer
Transduction is transfer by viruses that integrate into the genome then when they are activated, they carry bits of the genome attached to their own to a new host
Transformation is the uptake of naked plasmid DNA into a new host
Transfection is similar to transduction and is viral mediated
And of course you have acquired which results from point mutations that alter the cells ability to be harmed by an agent, simple changes like change of the cellular membrane or receptor sites