The three viruses
Hepatitis B is the hardiest — it can survive on surfaces for days and is highly infectious via tiny blood exposures; there is an effective vaccine, which every practitioner should have. Hepatitis C has no vaccine; transmission is mainly blood-to-blood. HIV is fragile outside the body and lower-risk from needlestick than HBV/HCV but serious. All three can be present without symptoms.
Universal precautions
Treat every client's blood and body fluid as potentially infectious. Gloves always; hand hygiene; sterile single-use needles opened in view and dropped into a puncture-proof sharps container; barrier film on all equipment; disinfect hard surfaces with an appropriate product; no eating or phones in the procedure zone; cover your own cuts.
Exposure plan
If skin is pierced or splashed: stop, wash/flush the area, encourage bleeding from a puncture, document, and seek medical assessment promptly — post-exposure prophylaxis for HIV is time-critical, and HBV/HCV baseline testing is needed. A written exposure-control plan is legally required in many jurisdictions.
Certification
A recognised bloodborne-pathogens course (often annual, OSHA-based in the US) is a licensing prerequisite almost everywhere — see the Training topic.