How do I give someone Power of Attorney to buy a Dubai property for me from my home country?

Draft a POA naming your representative, have it notarised locally, then apostilled (Hague countries) or attested by the UAE embassy, translated into Arabic, and finally registered at Dubai Courts. A Special POA covers one named property; a General POA covers many. Budget roughly AED 3,000-7,000 and 1-2 weeks (UK/US) or 2-4 weeks (India).