Inducer, e.g. rifampicin = a drug that stimulates the production of a CYP450 enzyme, e.g. CYP2C19. If a drug, e.g. warfarin is metabolised (into an inactive compound) by this enzyme, then warfarin will be metabolised more quickly under the influence of rifampicin. This means that the plasma concentration of warfarin will decrease, meaning that the INR will decrease (as the anticoagulant effect of warfarin is lessened). This will mean that the patient will be at an increased risk of DVT, PE etc. The easiest thing to do would probably be to increase the dose of warfarin whilst the patient is on rifampicin (dose according to INR) and keep a close eye on the INR and potential side effects of warfarin, like haemorrhage.
An inhibitor of the enzyme, e.g. erythromycin, will inhibit the production of the enzyme CYP2C19, meaning that warfarin will be metabolised very slowly, so its plasma concentration will increase with successive dosing, and hence the INR will increase. This will lead to an increased risk of side effects, e.g. haemorrhage. The best thing to do, again, would be to dose the warfarin according to INR, if this antibiotic is essential - if not, try and find a suitable alternative that won't interact with warfarin.*
Another example: a patient is on simvastatin, and drinks a glass of grapefruit juice with breakfast every morning. He starts to get muscle pains (without any obvious causes). Why?
It's also important to know that some drugs are activated by CYP450 enzymes too, e.g. codeine (into morphine), and clopidogrel. Therefore, if you inhibit the enzyme that metabolises them, you will decrease the plasma concentration of the active compound, and thus not get enough pain relief or enough antiplatelet effect. If you induce the enzyme that metabolises them, you will increase the plasma concentration of the active compound, and thus risk the onset of systemic side/toxic effects.
I'd say CYP2C19, 2D6 and 3A4 are good CYP450 isoenzymes to remember. It's probably good to also know a few common examples of inducers, e.g. phenytoin and rifampicin; and inhibitors, e.g. erythromycin, cimetidine (although rarely used now)
* EDIT: Antibiotics are probably a bad example to use here as all orally-administered antibiotics interact with warfarin - they can destroy gut flora, which are responsible for the absorption of very lipophilic drugs like warfarin through enterohepatic circulation.
Hope this helps!