The organism may lose affinity for the drug. Drugs act at particular sites on the organism. If the drug cannot bind to the site, it cannot destroy the organism. E.g Pneumococci that are resistant to penicillin develop altered penicillin binding proteins.
If the drug acts at a particular site or protein or enzyme, the organism stops using that protein or enzyme and adopts an alternative pathway. This type of resistance is seen in sulfonamides
Some organisms develop enzymes to destroy the drug e.g some bacteria produce beta lactamase, an enzyme that destroys penicillin and renders it inactive. Some organisms produce enzymes to destroy chloramphenicol or aminoglycosides.
Some organisms may not allow the entry of the drug i.e. they may become impermeable to the drug. E.g Plasmodium falciparum that causes malaria may develop resistance to the antimalarial drug chloroquine by preventing its entry.
Some organisms may throw out the absorbed drug. This resistance is seen for drugs like erythromycin and fluoroquinolones.