There are far too many species for it to be possible to discuss this group in much depth. Essentially it is imperative you know what species you have and what its natural habitat is and try to recreate this as closely as possible. This is the challenge for herpetologists.
Most species will need a heat gradient, a basking area with overhead heat (often an incandescent light), a UV strip at no more than 30cm above the reptile and appropriate food with calcium supplementation. Insect eating species must have well-fed insects (“gut loaded insects”). Imagine ourselves trying to get decent nutrition out of an emaciated cow! I would also recommend changing the UV bulb every 6 months without fail – despite what the manufacturer’s recommendation is and even if it still appears to work. It may not be producing enough or the correct wavelength of UV light for your reptile. Some species require special considerations – eg iguanas are arboreal and therefore will need height to climb, chameleons need dripping water to drink from. It is best to look on-line or buy a book about the particular species you own.
Shedding or Ecdysis can occasionally cause problems unless the humidity is right. Snakes tend to shed in one go, crawling out of their old skin. Lizards tend to shed piece-meal. Make sure their eyes have also cleared after shedding – do not be surprised if the skin colour and eyes become dull just prior to a shedding period and they are often inappetant.
SOME REPTILES ARE DANGEROUS. SOME ARE “CITES” PROTECTED – ALWAYS BUY FROM A REPUTABLE SUPPLIER.